{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to forecasting from scratch\n",
    "\n",
    "**First draft**\n",
    "\n",
    "In this chapter we are going to introduce time series and the primary purpose of time series modeling: forecasting. \n",
    "\n",
    " - Other uses of time series (anomaly detection, clustering, ...)\n",
    "\n",
    "**Disclaimer: for the sake of simplicity this notebook will gently abuse statistical notation**\n",
    "\n",
    "## Time series\n",
    "\n",
    "Time series have some unique properties that differentiate them from other types of data. These properties will shape the way we model time series data and the way we generate predictions. Let's start by stating the obvious: yesterday came before today. __Time series have a natural ordering__, there is a general a particular dependence between observations. This implies that we can use information from yesterday to model today's observation, but we cannot use information from today to model yesterday's observation.   \n",
    "\n",
    "\n",
    " - Discrete sampling (mixed frequencies?)\n",
    " - Regular/irregular sampling\n",
    " - Univariate/Multivariate models \n",
    " - Any data type\n",
    " - Dependence/dynamics\n",
    " - seasonality\n",
    "\n",
    "\n",
    "## Forecasting\n",
    "\n",
    "Forecasting is about using a model trained on observed data to predict future observations.\n",
    "\n",
    " - probabilistic forecasting\n",
    " - Measuring uncertainty\n",
    " - Target (mean, quantile, ...)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import mxnet as mx\n",
    "import mxnet.ndarray as nd\n",
    "from mxnet import autograd\n",
    "from mxnet import gluon\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "mx.random.seed(42)\n",
    "ctx = mx.cpu()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Deterministic features \n",
    "\n",
    "\n",
    "A deterministic feature is a feature that is known without uncertainty at any point in time. The simplest feature of this class that is used in almost every model (time series or not) is the intercept, which is simply a vector of ones at any point in time. Features of this kind are frequently included in time series models to capture regularities in the data.\n",
    "\n",
    "Our first model will make use of two deterministic features: a linear trend and a cyclical feature used to model seasonality.\n",
    "\n",
    "\n",
    "## Trends\n",
    "\n",
    "A trend is a feature $X$ equal to some function of the time index: $X_t=f(t)$. The simplest feature in this class is the linear trend, $X_t=t$: on a plot it takes the form of a straight line. This fearure is useful to capture some forms of growth. Other kinds of trends that are frequently used, alone or in combination, are:\n",
    "\n",
    " - Polynomial of order n: $X_t = t^n$, the linear trend is a special case with $n=1$, \n",
    " - Exponential: $X_t = exp(t)$,\n",
    " - Logarithmic: $X_t = log(t)$.\n",
    "\n",
    "One attractive property of this kind of features, as of any deterministic features, is that it is simply a function of the time index. Provided that the feature adequately captures the dynamics of the series it can be a powerful predictor for forecasting. Since the feature is a known function of the time index, it can be computed for any value of that index.\n",
    "\n",
    "## Seasonals\n",
    "\n",
    "Seasonality is a key concept in time series analysis and forecasting. Seasonality describes patterns in the data that recur at __regular__ intervals (for example daily, weekly, monthly) that can be caused by a number of factors such as weather, holidays, or the diurnal cycle. Adequately modeling seasonality is of paramount importance when building a forecasting model: seasonality is a regular pattern so a model that describes this pattern can also project it at any horizon.     \n",
    "\n",
    "Seasonality is often modeled using cyclical deterministic features, some examples are:\n",
    " \n",
    " - Trigonometric series with a selected periodicity, for example a sinusoidal with a period of 7 days to capture weekly seasonality. \n",
    " - Indicator dummies or kernels for special days.\n",
    " - Sets of fourier series to capture multiple seasonalities, possibly of unknown frequency.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " \n",
    "### Generate synthetic data\n",
    "\n",
    "Let's generate some synthetic data using only deterministic features: a linear trend and a sinusoid with a period of 7 days to mimic weekly seasonality. Below I set the parameters of the generative process and generate 110 observations, 100 which we will use to train the model and 10 to forecast.\n",
    "\n",
    "The model is $y_t = \\mu + \\beta X_t + \\gamma S_t + \\epsilon_t$, where $X_t=t$ is the linear trend and $S_t$ is our seasonal, sinusoidal, feature. The intercept $\\mu=1$, the loading on the trend is $\\beta=0.1$, the loading on the seasonal component $\\gamma=1$. Random Gaussian noise is added to the model, $\\epsilon\\sim\\mathcal{N}(0,\\sigma^2)$ with $\\sigma=0.5$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# periodicity of the seasonality\n",
    "seasonal_period = 7\n",
    "# dimensions\n",
    "train_length = 100\n",
    "pred_length = 50\n",
    "smpl_length = train_length + pred_length\n",
    "# set parameter values\n",
    "mu = 1\n",
    "beta = 0.1\n",
    "gamma = 1\n",
    "sigma = 0.5\n",
    "# generate the data\n",
    "X = nd.arange(smpl_length).reshape((smpl_length,1)) \n",
    "S = nd.sin(2*np.pi*nd.arange(smpl_length)/seasonal_period).reshape((smpl_length,1)) \n",
    "noise = nd.random_normal(shape=(smpl_length,1))\n",
    "y= mu + beta*X + gamma*S + sigma*noise\n",
    "\n",
    "features = nd.concat(X,S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_size = 4\n",
    "season_train_data = gluon.data.DataLoader(gluon.data.ArrayDataset(features, y),\n",
    "                                      batch_size=batch_size, shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the three components of the data (trend, seasonal, noise) as well as the resulting series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAD8CAYAAABw1c+bAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cc1a0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_components(data, trend, seasonal, noise):\n",
    "    plt.plot(data.asnumpy(), color=\"r\")\n",
    "    plt.plot(trend.asnumpy(), color=\"g\")\n",
    "    plt.plot(seasonal.asnumpy(), color=\"b\")\n",
    "    plt.plot(noise.asnumpy(), color=\"black\")\n",
    "    plt.legend([\"Data\", \"Trend\", \"Seasonality\", \"Noise\"]);\n",
    "\n",
    "%matplotlib inline\n",
    "plot_components(y,beta*X,mu + gamma*S,sigma*noise)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the model\n",
    "\n",
    "Just as in the chapter on `linear regression with Gluon` the linear model is defined by a single dense layer, but before the dense layer we need to add a batch normalization layer (cf the `Batch Normalization in gluon` chapter) to account for the fact that the scale of our data changes over time. \n",
    "\n",
    "We also initialize the parameters using a random Gaussian with variance 1.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "season_ctx = mx.cpu()\n",
    "season_net = gluon.nn.Sequential()\n",
    "\n",
    "with season_net.name_scope():\n",
    "    season_net.add(gluon.nn.BatchNorm(axis=1, center=False, scale=True))\n",
    "    season_net.add(gluon.nn.Dense(1, in_units=2))\n",
    "    \n",
    "season_net.collect_params().initialize(mx.init.Normal(sigma=1.), ctx=season_ctx)\n",
    "\n",
    "square_loss = gluon.loss.L2Loss()\n",
    "trainer = gluon.Trainer(season_net.collect_params(), 'sgd', {'learning_rate': 0.01})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sequential0_ (\n",
      "  Parameter sequential0_batchnorm0_gamma (shape=(0,), dtype=<class 'numpy.float32'>)\n",
      "  Parameter sequential0_batchnorm0_beta (shape=(0,), dtype=<class 'numpy.float32'>)\n",
      "  Parameter sequential0_batchnorm0_running_mean (shape=(0,), dtype=<class 'numpy.float32'>)\n",
      "  Parameter sequential0_batchnorm0_running_var (shape=(0,), dtype=<class 'numpy.float32'>)\n",
      "  Parameter sequential0_dense0_weight (shape=(1, 2), dtype=<class 'numpy.float32'>)\n",
      "  Parameter sequential0_dense0_bias (shape=(1,), dtype=<class 'numpy.float32'>)\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "print(season_net.collect_params())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Train the model for 30 epochs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0. Moving avg of MSE: 32.2507372604\n",
      "Epoch 10. Moving avg of MSE: 3.66994767658\n",
      "Epoch 20. Moving avg of MSE: 3.12723273528\n",
      "The type of \"params\" is a  <class 'mxnet.gluon.parameter.ParameterDict'>\n",
      "sequential0_batchnorm0_gamma \n",
      "[ 1.91860354  0.77953815]\n",
      "<NDArray 2 @cpu(0)>\n",
      "sequential0_batchnorm0_beta \n",
      "[ 0.  0.]\n",
      "<NDArray 2 @cpu(0)>\n",
      "sequential0_batchnorm0_running_mean \n",
      "[  7.53194580e+01  -2.02038828e-02]\n",
      "<NDArray 2 @cpu(0)>\n",
      "sequential0_batchnorm0_running_var \n",
      "[  1.12377185e+03   3.15755248e-01]\n",
      "<NDArray 2 @cpu(0)>\n",
      "sequential0_dense0_weight \n",
      "[[ 1.70669985  0.81172013]]\n",
      "<NDArray 1x2 @cpu(0)>\n",
      "sequential0_dense0_bias \n",
      "[ 8.41370487]\n",
      "<NDArray 1 @cpu(0)>\n"
     ]
    }
   ],
   "source": [
    "epochs = 30\n",
    "smoothing_constant = .01\n",
    "moving_loss = 0\n",
    "niter = 0\n",
    "loss_seq = []\n",
    "\n",
    "for e in range(epochs):\n",
    "    for i, (data, label) in enumerate(season_train_data):\n",
    "        data = data.as_in_context(season_ctx)\n",
    "        label = label.as_in_context(season_ctx)\n",
    "        with autograd.record():\n",
    "            output = season_net(data)\n",
    "            loss = square_loss(output, label)\n",
    "        loss.backward()\n",
    "        trainer.step(batch_size)\n",
    "        \n",
    "        ##########################\n",
    "        #  Keep a moving average of the losses\n",
    "        ##########################\n",
    "        niter +=1\n",
    "        curr_loss = nd.mean(loss).asscalar()\n",
    "        moving_loss = (1 - smoothing_constant) * moving_loss + (smoothing_constant) * curr_loss\n",
    "\n",
    "        # correct the bias from the moving averages\n",
    "        est_loss = moving_loss/(1-(1-smoothing_constant)**niter)\n",
    "        loss_seq.append(est_loss)\n",
    "    if e % 10 ==0:\n",
    "        print(\"Epoch %s. Moving avg of MSE: %s\" % (e, est_loss)) \n",
    "        \n",
    "        params = season_net.collect_params() # this returns a ParameterDict\n",
    "\n",
    "print('The type of \"params\" is a ',type(params))\n",
    "\n",
    "# A ParameterDict is a dictionary of Parameter class objects\n",
    "# therefore, here is how we can read off the parameters from it.\n",
    "\n",
    "for param in params.values():\n",
    "    print(param.name,param.data())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'est loss')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjMAAAGjCAYAAADZ3JQcAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108327278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the convergence of the estimated loss function \n",
    "%matplotlib inline\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure(num=None,figsize=(8, 6),dpi=80, facecolor='w', edgecolor='k')\n",
    "plt.semilogy(range(niter),loss_seq, '.')\n",
    "\n",
    "# adding some additional bells and whistles to the plot\n",
    "plt.grid(True,which=\"both\")\n",
    "plt.xlabel('iteration',fontsize=14)\n",
    "plt.ylabel('est loss',fontsize=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generating forecasts\n",
    "\n",
    "Now that we have estimated the model we can generate $\\tau$ forecasts for $t\\in[T+1, T+\\tau]$ as $\\hat y_t = \\hat\\mu + t\\hat\\beta$, or equivalently using the `gluon` model: `net(features[T+1:T+\\tau])` "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean squared forecast error :\n",
      "[ 0.13554694]\n",
      "<NDArray 1 @cpu(0)>\n"
     ]
    }
   ],
   "source": [
    "fit = season_net(features[:train_length,:])\n",
    "fct = season_net(features[train_length:,:])\n",
    "mse = nd.mean(square_loss(fct,y[train_length:]))\n",
    "print('Mean squared forecast error :%s' % mse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAD8CAYAAABw1c+bAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cddeb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_forecast(observed, fitted, forecasted):\n",
    "    plt.plot(fitted.asnumpy(), color=\"r\")\n",
    "    plt.plot(observed.asnumpy(), color=\"g\")\n",
    "    T = len(fitted)\n",
    "    plt.plot(np.arange(T, T+len(forecasted)), forecasted.asnumpy(), color=\"b\")\n",
    "    plt.legend([\"Fitted\", \"Observed\", \"Forecasted\"]);\n",
    "plot_forecast(y,fit,fct)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stochastic features and dynamic models\n",
    "\n",
    "\n",
    "The model we've used so far was purely deterministic and static in the sense that the value of the series at some point did not depend on its past values. In general a time series process will be dynamic, an observation at some point in time will depende on the values of previous observations. To model this kind of dependency we can include lags of the series, earlier observations aligned with the current one, for example noting $Ly_t$ the lag of $y_t$ we have $Ly_t = y_{t-1}$. $Ly_t$ is a stochastic feature, it had a random component, which implies that we cannot know its value at points in time outside of the observed sample.  \n",
    "\n",
    "\n",
    "The simplest class of dynamic models is known as autoregressive, or AR, models. In the remainder of this notebook we generate data using an autoregressive model, estimate its parameters, and use it for forecasting. This section ends with a discussion of the quantification of forecast uncertainty using analytical results or numerical procedures. \n",
    "\n",
    "## Autoregressive models\n",
    "\n",
    "An autoregressive model is a model in which the observation at time t, $y_t$ depends on past observations. The simplest model of this class is the autoregressive model of order 1, AR(1), meaning that $y_t$ is a function of $y_{t-1}$. This model can be written $y_t = \\alpha + \\beta y_{t-1} + \\epsilon$.\n",
    "\n",
    "### Estimating autoregressive models\n",
    "\n",
    "The AR(1) model is a linear model with two mean parameters ($\\alpha$, $\\beta$) and a variance parameter $\\sigma$. The simplest way of estimating the parameters of the AR(1) model is to use least squares, the same estimator we've used so far. \n",
    "\n",
    "\n",
    "\n",
    "For simplicity let's generate data from an AR(1) process recursively, with $\\alpha=1$, $\\beta=0.5$, $\\sigma=1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4wLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvpW3flQAAIABJREFUeJzsvXeUJNld5/u9YdJnVlV3mXYzbaZ7\nnMyMREszsggJgVgJ/wRiH2YXwTwWWGDhLGY5nDWYPSywgN7CgvZJj8ditKwWCa0YJEB+ZEbT0miM\nNKZ72tuqLp8+zH1/3Lg3bkRGRkZmRmVWZt/POXOmu7oqMyoy4hff+/397u9HKKVQKBQKxfSgjfsA\nFAqFQpEuKrArFArFlKECu0KhUEwZKrArFArFlKECu0KhUEwZKrArFArFlKECu0KhUEwZKrArFArF\nlKECu0KhUEwZxjjedH5+nh45cmQcb61QKBQTy5e+9KWblNKFXt83lsB+5MgRnDp1ahxvrVAoFBML\nIeRCku9TVoxCoVBMGSqwKxQKxZShArtCoVBMGSqwKxQKxZShArtCoVBMGSqwKxQKxZShArtCoVBM\nGSqwKxSKqeYTzy7j0lp93IcxUlRgVygUU81Pve9x/PGnXxj3YYwUFdgVCsVU07JcXFprjPswRooK\n7AqFYqqxXRdXNlRgVygUiqnAdSlcClxZb4BSOu7DGRkqsCsUiqnFcl0AQMNysFZrj/loRocK7AqF\nYmpxXF+l30p2jArsCoViarEcKbCvq8CuUCgUE4/tuOLPSrErFArFFCBbMZeVYlcoFIrJx1KBXaFQ\nKKYLZcUoFArFlGF7in0mb+LK+q3TL0YFdoVCMbXYXlXMkb0FbDVtbDetMR/RaFCBXaFQTC22t0Hp\n8N4igFvHjlGBfQpZ2W4FvEWF4lZFVuwAcPkWaQamAvuU0bIdfMNvfxL/68uXx30oCsXYUYpdMRXU\nWw6qLRvXNpvjPpSJYLNu4XNnbo77MBQ7BFfs+2ZyyBqaCuyKyaTtWTCNtjPmI5kM/urUJfzAe7+I\nphU8X03LwYefvHpLdQScRnhVjKERzBUy2Kyr5KliAmnbfjc7RW+qLRuOS9GygjmJTzy7jJ/8i8dx\n7mZtTEemSAPLEzqGriFjaEL4TDupBXZCiE4IeZwQ8uG0XlPRPy2bBfS6UuyJ4Dd6ywmer5p3/tQD\ncrLhLQVMnbDAbqvA3i8/DeCZFF9PMQAtpdj7wvLOl9wFkP2dfd12lBUzyfDPVdcITF0T98e0k0pg\nJ4QcAvBWAP9PGq+nGByuSJpKsSeCK/awkuN/t10V2CcZXhVjKitmIH4PwM8D6HrWCCEPEUJOEUJO\nrayspPS2ijA8ICkrJhn8fIUDu6/Yb41AMK04UvI0q2tihTbtDB3YCSFvA7BMKf1S3PdRSt9NKT1J\nKT25sLAw7NsquqCsmP7oqtgdpdinAW7FGJpS7P3yGgDfRgg5D+B9AN5ICPmzFF5XMQCiKkYp9kQI\nxe5EWzHWLRIIphVbVMWo5GlfUEp/iVJ6iFJ6BMA7AHycUvr9Qx+ZYiBEHbtS7InoZcU4SrFPNKKO\nXScwdaICu2IyUR57f/AA3l2xq8A+yQjFrmnIGPotY8UYab4YpfSTAD6Z5msq+kNUxSjFnohuHjsP\n6LyqQjGZyIo9oysrRjGh+BuUbLUdPgHdvHSehFZ17JON3FJAJU8VEwsPSC7ttBd2iicubeBn3vc4\n3An0o9te4O5a7jiBv5PCR7Zisip5qphU5GA+qsqYh5++hg9+5So2GpPXYEnVsU83smJXyVPFxCJf\nuKOqjLlwk82SrLXskbxfmrQ966pr8lQp9onGdig0AmjKilFMMnJgH1VlzPlV1gGxOoGB3eplxdwi\ngWBasVwXhs7CXEbX4bj0lihhVYF9ypCbHI3CiqGU4sIqU+z19uQF9m4blPh5vBWCwDTjOBSmRgAA\nGYOFu1th05kK7FOGrDxHUfK4st0Slk+1NXkllt3LHVUd+zRguxR6KLDfCh0eVWCfMkZtxZz31DoA\n1CfRiulS7ii6O94C6m6asRwXprBiWIC/FRKoKrBPGYGqmBEo9vPShKFJ9NhbPTYoqeTpZOO4FIYe\nVOy3QgJVBfYpo2U7Yuk5Co+dJ06ByauKoZSKgB5enreFxz79QWCasRwKQ/MUOw/sSrErJo227WI2\nbwIYjWK/sFrHgZkcAH+c3KQgbz4Kqzg1QWk6sF3XV+y6DkAlTxUTSMt2MeMF9tF47DWcWCrD0EhA\nsfPWBrsZWbmFBzC0VfJ0KrBdCsNbwZrKY1dMKm3bxUyBBfadrorhpY5H54soZHTxIHnk9E3c9+//\nHmu19o6+/7DIN3i3DUqqCdhkYztuhxWjqmIUE0fbcVHKGtA1suN15au1NqotG4f3FlDKGiJ5emZ5\nG03LxfJ2c0fff1jkJbnqFTOd2E5E8lQFdsWk0bJcZA0NeVNHo80u4B//8y/h7566lvp7XfASp0fm\niyhmDWHFbDbY/2u7vK5dVm6q3HE6ka2YrKqKUUwqbcdFxtCQM3U0LBtNy8HDT13HF86upv5e57we\nMUf2FlHIGiJ5uuk1A9vtO1HlGzy8PBf92JXHPtHYoZYCQGc+ZRpRgX3KaNsuMrqGQkZHo+1g1fO5\nd2JX6MXVGjQCHJzNo5TVJcXOAvtuV+zdrBhKqZ88VVZMgLbtTlSbBduRkqeGlzxVil0xabRtptjz\npo6G5eDmdgsAUG2l31L3ykYTS5UcMoaGQsboCOy7XrF3SZ7KlTCqjj3I2//oc/jtv39uLO99dqXa\n98/Y8gYlXXnsigmlZTvIGjryXpXKzSoL7Duhnq9uNHBgNg8AKGUN1LxAvtX0FPsur2vnN3hG1wLq\n3eoS5BXAmeUqnr6yKf7+7PUtnJN2H+8UX726iTf+zqfw5OWNvn4uqipGBXbFxCEr9qblB/ad2O5/\nddMP7MWsLh4eW8KK2eWK3QvgxaweVO/Sn1Xy1MdyXNTaDq5t+tVOP/O+r+A3Hn5mx997xVt5yu+d\nBNulon5dlDsO+Jk2LQfX+3z/cXFLBHZKKV4YYBk3ifDkaUEoduaxpxFkG21HlDC6LsW1jSYOzLJd\np8UoK2a3B3YvgJdyRnCzknTjq3JHH/7AvrrRAKVU7GMYxQOcJ7e3m/29l+343R2zoeTpZsPq69h/\n4+Fn8Lr/9HH8z1OX+jqGcXBLBPZTF9bxpt/5FJ6/sT3uQ9lRXJfCcigyuoZchnnsXOmkcfP9wSfO\n4Nv+78+CUoqbtRbajouDQrEbaNkubMf1k6cTYsWUsmYgsLcCil0Fds6GyJ042GxYuFlto2E5I7E2\n+GdSbfaXK5IHbYSTpw/96Sn88geeSvQ6tuPifz9xFYQQ/Ov3P4l3fex0X8cxam6JwH51owEAE7OM\nGhR+wWYMDQWTVcVwK2Y7hcB+s9rC9a0mVrZbuLrBzuWBGRbYCxmmhjYaltiB2m/y1HJcfM8ffx6f\ne+Hm0Mea7P1Y0C5ldTHUmh8HZzfsPH3/ly6PxO7oxaY00/bKRgMX11i56yh2cvJd1P0qdseVBm2E\nkqfXNpt44vJm15+V+fzZVazXLfzu99yPb7p3Cb/3j8/vaq/+lgjs/ILs96KYNPgNljU05D3F7idP\nbVA6nPrkF/Lp5ap4WMrJUwC4tuE/PPtN2K7V2vjiuTV89sxoAnvbYcdXzBpi9in7+miSp7/90efw\n549eiP2eKxsN/MoHn8ZffvHijh1HUuTAfnWjicvrLLCPVLH3KVCYFcPCnKFr0Ih/vPW2jQurtUSt\nNx5+6hqKGR1vumcRb7hrES6FuLd2I7dEYN8SgT39kr/dRDsU2GWP3aVA0xruBuQB7/kb21Jg9zx2\nL7Bf3WyI7+9XsXO76OrGaFZWvhVjBIO57QfznVTsH3riKj72zHLs9/z6334NDcvBdtMee2O1rUBg\nb+CSUOw7f1wtL/hu9SnO2KANIv4uD7SutRy4FD3zb7bj4iNPX8eb7llCztSxVMkCAG5s7V4H4NYI\n7N7FMImDIPpBtmLyJqv0WN5qig0aw/7+smK/stFAIaOLTpLFLLNieMAH+lfs/PuvrDd6fGc6tIUV\nY0TWtGcNbUc99lrLjs19PHL6Jh5+6jqOzRcBQDRVe+LSBv7Lx0fv8W7Uw4GdfU67WbHLgzYAwNQ1\ntG0XrktFW+szy/GBndswb33pfgDAUoWJmeXtKVbshJAcIeSLhJAnCCFfJYT8+zQOLE02vQuy36f9\npCHqsr2qGID9zrftKQBIIbB7Ae/MjaqoYSeE3TTFjGfFeHmMSs7oX7F7339lY0SB3ebljgZc6g+u\nlr++k1Ux1ZYd21r5r05dwnwpg595850AgFVv9fXXX76M3/mH54e21vqFWzGH5vK4stHApfVxeOx9\nJk+lOnaAPazbjhuYVdCrqOLjzy4jb+r4+jsXAACLZabYl6dcsbcAvJFSeh+A+wG8hRDyYAqvmxp8\nw8ytY8XoyJu6+PrhvSywD1sZw1//+eVtXJE2JwG+FXNF8t77rYrhx3d9qzmSbeuyFSP/nSdP86a+\nY3XsluOiZbviYRbFdtPC/pk8Dnp2F/d0l7dboHT07Wc3GxYKGR237ykwxT4Gj73vckepCRjAEqjt\n0Hk/fSNesa/V2liqZJHz7qm9pSw0AtzYmmLFThn8zJjef7uqRswP7NOt2LnXmdE15D0FDbAmXcDw\nip0HvI26hedvVEXAASSP3Qvs+2dyfdex8weB49KRtPzlv084sPP/FzL6jiVP+UOsHmNX1doOChkd\ne4tMIXIrhlsArSFzJv2y2bAwmzdxYDaPi2sNkQsZdMNPP3DFXh0gsOthj912xXnXCLMW46i1nMD9\npGsEC+Xsrm5LnYrHTgjRCSFfAbAM4B8opY+m8bppwZeQ/V4Uu4Frmw388J88Jh5OcchWzE4p9qy0\nLZuXOgK+x86rYvYPodiBoFe/U7RtFxoBcp5t5U9N8gP7Tq0cuMiIU+wNHthLGQC+FcOTds0RJ1M3\n6hYqXmC/WW3BcSn2VXJo2+6O20L8Idbvqtt2XJiSFcMDOz/vdy6Ve1bGNCwbxYwe+NpiOTfdih0A\nKKUOpfR+AIcAvJIQ8uLw9xBCHiKEnCKEnFpZWUnjbROz5fUH396BRlg7zeMXN/DxZ5fxzNWtnt8b\nCOwZ/6M9Mp+OYm/ZLu7eXxF/D1gxnqK5sd1E3tQxmzcHrooBWIOxnYbv0s3owY0r/P/5jL5jVTE8\nsNTbTtegWGvbKGQNlLIGMrqGm7UWKKVCse/0hKwwWw0LM3kzsFK7Y5FdWzvdMZE/xPrZj+G6FC5F\nZ/LUccWg9/sOzcKlwNmV7v1umGIPBvalSvbWqYqhlG4A+ASAt0T827sppScppScXFhbSfNueTLIV\n0wj1OI+jFaiKSd+KaTsuDs3mUcmx15YDe97UQQhAKTCTN1HMGrAc2pf/KlfRjEqxZ3StozmUSJ5m\njB2zYvjq0XFp16BYbzkomDoIIdhbymC12sZWwxbHN4ph5TKbXmCXP/fjCyUAO+/3c8VebdlwE66i\neOI74LEbmuh5AwD33z4LADi93D2B2mg7QrhwFiu5qa+KWSCEzHp/zgN4M4Bnh33dtHBdKupvJ9GK\nqfdRv8svfl7HDjA7YcHL4qdhxWQMDSeWygAg2gkAgKYRFDz7ZyZviqqcflR7vW0ja2io5IzRBHah\n2D0rxo5Q7DukROWHbDefvd62Re6CBfZWwNcddl9Cv2w2LMwW/MCuawSHPdGw0wlUrtgp9e+JXvDV\nFm8pALD8U8t2Rf7nRQcqMDQSWxlTa9vieuYslXNYq7V37e7TNBT7fgCfIIQ8CeAxMI/9wym8birU\n2jb4A34Syx2bfSh2uf6aX4jzpawIuMMO27AcpnBPLJZACLA0kw38Ow9CM3lTKJx+fPZqiwWyA7P5\nsSh27q1bUvJ0p8od5cDezWevt30LYG8xi9VaO6ASR23FbDTaTLF7uZX9MzmRWxmVYgeS++zdFDvz\n2Nm5m81ncGS+iOdjKmMabQeFbMhj9zYprezS3adG72+Jh1L6JICXpXAsOwIP5rMFcyLLHev9BHbR\nX5zZIgAwX8pA0wjrl56SYv+BVx3GfbfNImsEL/ZS1sDydguVvCkCUj+VMfW2g2JWx8HZ/Eg8dstT\n7HxnIg9O3H4pZHaujl3+LKJq2du2C9ulImm3t5TBmeVqSLGPLrC3bAdNy8WM99nuKWZw21xBXAM7\nrVzl3a3Vpg3M9P4ZvrlMDuxZQ8Oq7aLhPUzzGR13LZXx9NXuPWOYYg+GSnn3qbxy3S1M/c5Tvjnp\n4GweLdvdtUunbnAfdaufwC5ZMfMldgEWs/rQVhQP7HculfF9r7y949+5qmEeO/tz34o9M1rFbkZ5\n7KGqmJ2o+JDzPVEPXG5h8YAyX8pitdYKVGKM0orhwoLvNP7eV9yGb7//gN/jfIcrdJqWK5p4JV15\ncxtNtmJ48pRfl8Wsjrv2lXFxLbr9sONSNC23w4pZLHu7T3dpZczUB3aeOOVP1UlrK8CVRTLF7tWx\nS+WO82Ue2A1UhxxV13ZYIOwGt1+Yx87+3J9i962YzYa1458Vf1CFp9fzAM/P4U4kUOVEcZRi54GH\nB5Q9xQyalovz0rSiUSp2LixmCqz08hfecjfe8crbA+WvO0nLdjDvlX0mvS74aivcK8ZymMdOCJAz\nWGCnNHoHKhdWHR67aCuwOytjpj+wexfkwTkW2CfNjuEXVqKqGLkJmKmjnDVw2GsnMKwVQ6nX692I\nCexDe+ysbps3Fru2w6q9LawYz2OXFLupE6H0dqKWXZ5BG/W58Ad6gSdPiyyoPXNtSwTTUQZ23ieG\nK3aOr9h3OHlquUKkJPbYvQeyrgWTp9xjL5g6NI3gnn2shPe5652BPbxy4uwtZqBrZNeWPE59YOcB\nkSv2SSt5bFj+tJdeyFaMphH83c+8Dj/06iMAhg/scmK2G35gN4Qt01dVTMtGKWvgkPcQ3umeMR3l\njlLy1NR9793agVr2ai/F7v07T3xzS+25G9ui988oA3vYiuGMzmN3xTnodg8/fnFdlAcD/ufW0d3R\ndlFvO+KheWguj0JGx7NRgb0Vrdg1jWChlFVWzLjgftyhOXYzpBXYN+tW4CLaKfqyYhwXhPjJokNz\nBdHfopg1hvrd5cHP3Shxj70gKfaYSpytpoW3vusz+KqXuKq1WJKKl9PtdPtev9yx02PPGJo4jzvR\n4bHasoXVE1UVw4M9f0Dy3adNyxWrsOYI80XdAvuoPPaWJVkxEdfxRr2N7/6vn8MHv3JFfM0RVTGd\nO0/rUgmjphHcuVTuoth5YO+sM1mqZHFjl9ayT39gb1ggxO8bnpYV84PvfRS/9rdfS+W14ujHiuEK\nlHdclClljdjt60leGwiqnzAF2WNPoNhP36jiq1e38OUL6wCYbVPK6ljwlNlO+5e8fLNDsXu5BG7F\n7EQte61li8qKqDr2sAWwt+SXlnLFPgphweHX32yHYh+Vx+5iTzELQqLv4ZXtFlwaLDLg5at6qAlY\ny3FRazmBYH33vjKevb7VkSj3P4egYgeAhXJu13Z4nPrAvtmwUMoaqOTYBZlWQu7aZrNnV7g06Kfc\nseUlA6MoZvW++6PL+L3eOy9w/z2kwM7VaMx7rniBe7XWBqWUKfasAUNnCc2dDlw8edqh2G02N1Yo\n9p3w2Ju22DgWZcXwr4lyR89jB4B9MzlkdG2kvWK4x14Zg8fOd+fmTR2ljBHZVmDdO76oebWRydN2\nsP/L3fvKWK9bYkYwpy5Vz4TZzW0Fpj6wbzUtVHImyt42+LSsmIblBKYF7RQ8uLVtt6en2rLdjtpy\nTjFrDPVQ41OFYpOnGb/ckQfnOMXOS/fWam20HVa3zTstFrwJUDtJXLljxpAV+85YMTN5Ezkz+hzV\nQ8nTnKmLc7NYziJnaiPt7rjZsFDOGgH1C/jW3E4GdtGO2tRQzkVbirzzpbxy4A/ksGKnlMUFfm4B\n4C4vgRr22fnnILfo4CyWc1ivW7uyhHr6A3uD3UAlEdjTsWKaloMbW83EfSuGeR9OL9Uud18MU/am\nBA16EfL5oHGB/eBcHllDw0LJH5cXZ/8sS4q9FkpSFTLDWUdJ4FU+UcnTzI4nT1lpZ7ffM5w8BVjJ\nI8ACSs7UEydP620b/+3TZ4cKQFsNq0OtAyzYAjtrxfDfM2toKOWMrh47EGxGxi00uUSXf9brNatD\nsQOdlTFxin22wM7Hbqy0uwUCu4VK3kDW0JExtL66w3XDclxYDiv/u1nb2eRJve0IpdZrkxJXmlFw\nm2TQyphWguTpP3nxfnzmF74BM94FX8josf3GeUXBWrUtjqsoKfadtmJaISsmUO5oEJF02wnFXvMq\ngLqdI1E/LQUUnkBd9IY+JG0C9v9+9jx+/eFn8LkXBh8SvuE1AAuT1Xe+pQB/7Zypo5wzI7u0rnmB\nvSWdk6iWAjzIb9TbgY6Nc8UMFstZPHM92EWVl+uGuzsCQCXv3Ze7sNJu+gO7Z8UAbFxbGlaMrJSu\n7XDlRsNysG+GKeDeit3pGnh5wBzUjvFLKbsnTzWNiB15ANuwFKe6eUXBWq0tvo9X04zGimHnS9cI\nCOlMnurCY08/aG17gb3bOaq1bOgaCXyefOAGt2KSKHbLcfGnnz8PADh3s3tr2l7wBmBhRq7Ys90U\nO7s3AoqdB/aQxw6wgB3u2HjHQgkXVuuBrzVC16VMOcvOR5Jd4aNm+gO7pDTKOTOVwC4rpWs77LM3\n2g72VZIF9rjkKVf9g9obfPcl74SYhEI2PjjzigLZiuFL3kKm/5mp/cKtGEKI2LgCeOdRsmLSVuyW\nwyyxUtboeo7q3pANucJpvpRBxtBYvxZTT9RS4OGnrolcxrCBPUqx+x77zj2Eg4o9Wpytex57MHnq\ntRTQOq0YAB2NvUo5o+Oz4NelPLiGw62p3bg3ZuoD+6bkDZayRip+WLPtXzw7WWtteQnF5Iq9u8de\nGtKKkTc/JaWYid8UxSsQ1uttsZIojjJ56vj9RzKGJjUBCyVPXRfXNht4y+99OpUHuWw7dTtHrGoj\nqBJ/4FWH8Wvf8WIQQpBN4LFTSvGeR87h2EIRLzk4syOBXdMITJ3sqGLnD42soXlWTFRVTGfylIsR\nWbHL90f4/OZNXSh0Tr3N9htoWudK1bdilGIfKbbX7IdbMeUuiZd+kRX79R0sd+KBLalib8codh4w\no9TFex45h786dSn+tRMkT8PEBWfLcbFaa6OSM+C4VLQP4Ddbfoc9dselcFwqPNeMrom6Z74fwPRu\nZsuheO76Np69vo1nr8VPtE8C/wxKOaPrOeKKXeZFB2bwPSdvA4BEydMnL2/iycub+OevOYpjC8Wh\nAnu95feGD8N7nO8UfGXiK/bO+yCq3DFyg5JkbYXPbyHTmbfgHUej4HFFWTEjhic1Zrwna7dlXL/I\nFsFOdiHkNy7fyNIzsMckT33F3hkM/uwLF/Chr1yNf+0EG5TCxFXFcLV+jzdqj0+85zdRL3+e85Gn\nr+FzZ5InBT/4+BX88J88JoI4P198RyLQ6bGzDn/9j2brBv+9Slmj6zmqR/QAl8kZWk8r5plrLBH4\nDXct4Oh8EVc2GgO3IWjFrAazpj46xZ410LRc8flx1iPLHXl3x87kKdC5mzRndooJuSd+GO4EKMU+\nYviTtBLw2C1cWqvjtb/58dipKXHwp7qhEVzb3DnF3hClVgbKWSOZYu+aPOUbhoJBhFKKG1vNnjd8\n21vWxvWKCRNXFbMcCuwX1zzFnvUVexIr5rc++hz+6NNnEx/To+dW8fFnl8W1EQjsInlKA1aM5bji\nMx+2pz3gb4mPq4qptWwUImqnOfmM3nOD0tXNJhuIUsnh6HwRlAIX1+qxPxOF7VmCuQifGeCKPdkD\n49T5Nfznv3+ur/dvislguihbDq+8o6wYsUGpi8ceVuL5TGfeIsoSEz+f0aER5bGPHP4k5UumUpbt\nWvvQE1dxeb0hFE2/8CB4+95Cah0IN+sWPvL09cDX/D4VOip5M5XkabVl4+pGQyxnqy0b9bbTM0jI\nQzySEqfYeeKU1w9f8gKOXBXTiBn0zNmoW4l25crfDwDnveoHEdhDVowZSp42vLxKGlaenE8oZjsT\ndgATD/GKvbcVc32zgYVSFqau4dg8m00aN7S5G3LX0CiyppZYsf/vJ67iXR8/09eOTf7QyJnMYweC\nwdRxKTYaVuB7AV+x6xFVMUCnYs+bOtsoJ60G4hQ7IQTlnKmsmLSwvS3BvRCNiwp+uWO1ZePhp64B\nGNwb4zf5sfkSbmy3Umnr+tePX8aP/dmXxA46wF8Z5EwdM/neF1C7x85TAPj4s8t44+98Er/x8DMA\n/N2fvZb1gyRPC54Cijo/N8JWzFodGmE3Lz9eO2bQM8BWGxsNC9t9fI5c2Z1fZQEu4930plQVwywt\nqY7ddVO1YnhgL+cMlrCznI5zxBqixQR2s7cVc22zif1eQ7Uj86y/zCA+e1O6DqPox2PnAfkLZ1f7\neH9JsfNckVTLvtWwwJ//8vViCcUeHdiLofPLK19kn70eURYpU8kbqo49Ld7zyDl80+9+uuf3bTX8\nG4j93wSlwFevMqXej9KT4R/8HQtFOC7t6C8xCPxY+Q46wLdiChkDM0MqdtPb4v/ImZtoWi5eWGY3\nOFfOvRKV8hCPpPAbIuohvLLFbIITS0xJrtbaKGYMUd4nbrKY49pq2nBcOpBiv8ADu2TF8ODELS3u\nzdouFZ95Goo9UBWT7QwmgDdnMyagyBuUXlip4j/+3TMdzcqubjRwwKuoKudMzJeygUEdSUlTsfMg\n+PkXkgd2WbFXIlqDrEn3TDsieRpuKcAJK3H+d/mzqLXsroodYG6AUuwp8cJKFVc2Gj2X6TWhjDwr\nJuffKBoZfMcY/+CPLbAJ7Wn0jOHBTz4m/j55U0cln8Rjd2I98INzebzyyB584z1LuOwlK3lVTy+P\ntC22ZydPnvodHjtfe3m7xQZtZwyhwuSqC65W43x2PvZws2ElHl/Hz6GwYjxrKSp5Krft5aq1GrHr\nsV9EVUzG6Dppim2giVPsLGHpuhQfefo6/vhTZ/F3kpVHKcW1zaYolQWAY/PdK2NO39juSEhyRGA3\no6+t/hQ7O3+fH1CxR1kxXAz4S2psAAAgAElEQVTNFczAcfDfRx6NF/TYO60YIFjO3LDiP4e0CjLS\nZiID+3qdLb16jSzjy+ZSxq+KAdjyf6GcFYGhX5ptHtiZ2kxj9yn3ouWnvwjsGX1oxQ4AH/6Xr8X7\nHnoQ9+4v4/pWE5bjJrZixAalARR7VMLxxlYTi153Q94DRfaUeYOmOMuN2yqyou5FWLHzB1VHuaM8\nWclxxcohje6g8masbrNh620b+R6KHWCfOQ9sf/jJF8QDbqvJcicHZvxBy0fmCzgbEdivbTbwlt//\nDD78ZHRllLBiuth8WSN5VQwPghdW64krykRVjKlFFgGs1dhnulTJRTYBC3R3jCl3jFbsTuznUMmZ\nqiomLXhA7pXw85e87APjT/tvefG+oT4QodjnmWLvZ9PK+790GT/03i92fJ1XRsjBW56k3iuwU8r8\n6DjFXsgY0DSCQ3MFuBS4vtkUSawknSOB+F4xYfgW9Ciranm71RHYS7JiN3sr9nVpCZ7Ejmlajvjs\nzt8MJU+9qhjXpbC9+vYoKyYNdVZtWciZrOqmEPHwa9usF1G8YvfH4/GH1TPXtvCp51cA+Nfk/llf\nsR+dL+FmtdVx3T91eROOS7FabSOKnordYD3Ok7DdskTCPKkd4yt2za+Kkc4Xvw7CgT3SiumxQQkI\nBvZGqL1vmEqC3Nc4mMjAzj/IXsGo2rLFDQQALz5QwetOzOP/+LpDiRRwN+pt1mNkTzGDvKn3VfL4\nlUvr+PTplY6ukPxClW86rhLzXvK0abldLRPbpaA0WeDlo+curddFh0XbpbEDJeKGeHTjxBK7gU8v\nd/atX95uiYHAvNe4rKCSWDEb0ooryWcpfw8/33JVTNt2RSfHjCH3iqHplju2HJS8PiN+HkIOJt0b\nT3FyUhDaaFi4Y6GI/TM5/OEnXwAAcU3un5EDOxMi50KVMc94m6662Sm9FbsWaL4VR7Vp4+SROcwW\nzMQJ1JbtiNYPcnUXh9ew76vkIq2YbuWO4aqjnBAT7LUppahbnRvFZJhAVFZMKojSph72QbVlixsI\nYFNo/vs7H8CB2Tx70g6o2JuWg5zJLrT9Mzlc7yOwNy0XlHYqP35j8yQqANSlCel8O7f87zL9VK3w\nMYGX1xvCigHiR62xEsDkQR0ADszkUMoaOB3aL2A7LlarPRR7H1YM0P28yPAHAd/JCyDQUkBua8x2\nnvoTlHyPPZ2qGD5GsCCsGPlzD7ZXiEL4wZaDjXobC+Usfvg1R/HFc2s4f7Mm7MH9khVzz372oH3y\nymbgtb52jf29W6I6iWKPq17iUEqx3WRttB84uiexz96yXOS86zpvstrxWkCxW8joGuaKmY46do0g\n0A6A22vhBmuALyb4Z83v1ULM51D2Ku12YuD5MExcYKeUCk+xV8Kv2vRvoDDDKPaGVNtazBqJ/V3A\nX+bJQQmQPHbpYdNsOyCEKSK+yarbMfcT2PfN5KARFtjlh1LcCsiK2dXaDUIIji+W8FwosK/W2nAp\nsOAF2D0lrtj7S572q9j5dXPvgYr4Gv+dTF0TrZjZ34lvxTjU99hTqorhloJQ7K2grwtEj2Pj+FaM\ni426hdl8Bm+4awEA8Nj5NVzbbEAjEA9PALh9TwH7Kjk8GgqoXLF3+/z97ordPfYkQz+aFtvoVM6Z\nOHl4Dy6vN4TajqNlO8h6DzJCSMf83vVaG7MFUzxgeJ7BdmmgnQA7Vvb3cIM1QPLYveQpvydjFbt3\nX6ZxXaTJxAX2WtsRN1+vhJ98A4Wp5IxEKi+KhuUIxWTopGs1QRR8yboRCkT8xpb9unqbvQ8hRCj2\nzUb0jZDkIuRkDA1LlRwurzErhlshcYE9rg9NHHculTpGCHKbYMkLOvz9ZYXKz29cP/eNCI/9yxfX\nuy7x+Tm/d39nYOfljv4DUveTp66/8zSVOvamHdiIBQQVu1zm2g0e6Jo2s2LmiibuWChhtmDi1Pl1\nXNtsYrGcC1SEEELwwLE9ePTcmgh+201L7EbtJlD87orDKXZeEVPKGjjulbmeWek9XrJpuYH3LmeN\nkGJvY08xI4I2P17bcQPtBAB/hRZVmx722JN8Drz8crclUCcusMs3cy/Fvt3qvh14xrNiBpmA1LAc\n4cfJG1uSwB9GG10Ve7DckV9s894w45tdElxcwfBdtr04NJfHU1c2YTkUt+8tBI4tirg+NHHcuVTG\naq2N1apv+Zy7yW5m7vnu8fqMy0mqYiIrxu8RzgP7b/7ds/h3H/pq5PfzpPs9UmDnwTtraGjbju/L\n6sTvFeNQNLxzU23ZiUsru1Ft2aJCqyBUoqTYRQ/w+J2nAFvVbdYtzOQz0DSCk4fn8NgFptjlxCnn\ngaN7sbLdEmWP8sSgbp9/q6diT+ax82u7nDNwYpEF9iRzg1u2E3jv8JjHDe86EIO1vc+QKfZgYNc0\nAkMjkbt6c6HA3o9iH3T1v1MMHdgJIbcRQj5BCPkaIeSrhJCfTuPAuiEvv3st/2rSDRSmkmeblaoD\n9PxuWr4Vk9G1voYd84tmI1RqyRVIuNyRvw9fUnfbDBXui9OLQ3MFkdQ8spcF2F6K3eyjIoZzp5dA\nfV66gc+u1KARiAdKlGIXVkzMMa3X27jNyxfw3//GVhNXupTRbXirHe41A76CM3UCy6F+9Y/h17Fb\nLhUlrpTG20NJqLX9TolispXssUvVUN3g/7ZWZ/Ni+QPu5JE9OLtSw7PXtgOJU84Dx/YAAL5wdg0A\n8DWvrUYpa3S3Ynp47Nk+FXslZ+LATB6FjI7Ty737NbVCir2UCwb2NU+xh2fX2q4bWLFwMoYWGax9\nK4a9ttzSoxvlKVbsNoCfo5TeC+BBAD9BCLk3hdeNRPame5U78rmSUYgn7QC17I324FZMUwT2sGKP\nKnf032dPMQNCYgK7pIaSwCtjAOa9yscWBR8+0S93isoY/wY+e7OG2/YUhArbIwK7fwNlDQ2E9LJi\nLOwtZUSDNNbQrIXtph15o63XLRgaweG9RZEIzkpWTNvxuwbyCiBDI7ClJmDA8AlU+XPNGhq00O/p\nz9mMq2Nnx81zJHNeYH/FERa4V2vtQOKUc2y+iPlSFo+eY3bVM9e2MFswcXhvoevn30uxcxur10pm\nW7pGNY3gjoUSznji4tzNGn71w1+LXEE3Q4q91KHY25gtRFkxnYodYKu0KHvF3+3Mfr7eSmLF7M5h\nG0MHdkrpNUrpl70/bwN4BsDBYV+3G7LSTeSxdwvsucFbbjakEqh+rZhGhMfOJ+qEj0dW7IauYW8x\ng5VqdGDfDjU864Uc2A+HrBhKO0sfrR418t1YqmRRzhmBTppnV2piDwD7HqYsZwsZ8TVCCIqZ6AZZ\nnPV6G3OFjKglrrZscX6vrHeqdr5k1zUidmT6/dj1QHterv4MnYhyR26NDHsTyy1w+e8ZUOwxU3s4\n3IrhgX0mz87diw9WxGtHKXbhs59lPvvXrm3jnn0V0bOm2/EC3T32rKGBUvRcufqBnV2jJxb9wP6n\nnz+P9zxyDje2OyvMOhS75LFTSrFetzDnJU8BWbHTyFVmxtAibS5dI8gYmjgP9QRWjF+tNn2KXUAI\nOQLgZQAeTfN1Zfry2JvdA/vMEN6Y7LHLOxaT0BIeezBJygmUO0rKDmA++/JWelYMJ6zY/80HnsZ3\n/9HnA7/XoMlTQgjuXCrj+evsBnZdinM3q2LXLsCqdP7iRx7At913IPCz+YyOhtU9iG56gZrnS+TS\nzajAvtloi8+d78iUk6eAX5HCA4KhaaylQNvBgmeHDVvLLld5AN4IwYBi713uyK+/a94GM27FZA0d\n9902CwCRih0AHjy6B9e3mviLL17Ec9e3cM/+iteytrtiJ6T7HolMSCl3g4sPvqq8Y7GEa5tNbDct\nPHKa9dSPOrdhxV6U5p7yfkFzhYxoD9GWkqd6hGLPdFHsALyRgzyw97ZifIE4ZYqdQwgpAfhfAH6G\nUtrRD5cQ8hAh5BQh5NTKysrA77OeULFbjouWN1cyCjHWaoDKGHkpbXqKLilRVgy/kWdCtfWylw8A\nC+VsjGIfzIrZU8wIBcWtrbMrVTxxaQN//KkXxPcPmjwFWGXM88vbrH/JVhNNyxV9djivPj7f0T2w\nkNEjB4MA7PPdbtmYzWdEH51lqRVsVP8eptiZsj0wGwzs3JrhwUcEdp3A9qpieGAfxoqhlPn4Oelc\nhhV7LUFA4defb8X4q51XHJkDgMjkKQC8/s4FmDrBL3/gaTQtF/fdNoOsoYsEcZimt8LotjmNB91e\nK9fwNcoTqJ89syryPdWIz7tlBVeLvP024G9OmgtYMew1LJd2VMUAwE+96Tj+6QO3Rx5jXhq2kcQS\n41V3U6nYCSEmWFD/c0rpX0d9D6X03ZTSk5TSkwsLCwO/VzB52l2xyx30ohhmCRW2SKwhrRgevPbP\nsC3RPPg3QuPRFss53OzqsVvIm3riBOf+mTwI8SfeA/6DkgeZd33sDM543vigyVOA+ewbdQsr1RbO\nrgQrYuIoxFgx/DqYK5piT4K8jO9mxXAv+uh8EcWMLjxYvkv27792A4BkxWgaGm0HtktFYB/GirEc\ntkM4rNhlpdpoO9BI/FCTbMhj54odAL71vgN48Nge3LVUjvzZw3uL+NKvvBn/+LOvx4d+8jV420sP\nIJ/Ru95PLcvp6q8DsmLvtYK2QIhfasjP+f/3ufPie8LN0AAmOOSHPrdimA3DAntU8tTp4rF/7ytu\nx2uOz0ceYz6ji4R9kiS2rhFvlvKUKXbCHuPvAfAMpfQ/D39I8WzU237ddUxA5aqqu2IfwmMPKHZN\nTBfqBaW+hyuvPPhNzT1Rfkz1dvCCXihnsbLdikxSbTW6VwBFkTE07KvksFTJBXYxsuNx8Kpje1HI\n6vgPH2Z92y1nsOQpwGZ1AsAXz62JQQ93SFZMNwoxVgxf8cwWMl6velvYVAvlLC5HVMawgczs2nnn\na4/ib37yNUKFvu74PI4vlvChJ1gjLLlaht+0C6XhFXtTGvPGYYo9WO4otzCOgieXeUsIedD03fsq\neN9Dr4pVmpWcieOLZbz00Cx0jSAnecth4sbiyb9LL8W+5VmjfCfobXN5ZHQtsAM16tx2KPacAZcy\nkbQuroMoj93t2KDUiyjFXojJdQDenpgprIp5DYAfAPBGQshXvP/+SQqvG8l6vY1FL9kWV+4oAnuX\nYFfKGNBI/x6763pLaeGxJ6+KaTsuuGuzKVkxXCHv8zxRbg81Q30qFspZtB038pi3W1Zif53z82+5\nCz/6umP+ZhepH8rhvQW8+Z4lPH/dV+yDWjFfd3gOS5UsPvj4FZxdqaKY0QM7IrsRZ8XwB+NcwUQl\n5yn2rRZKWQN3LpUiFft6vS2UbTFr4Piir2g1jeBHXntUbA3nv6uuEXEtCSsm5iamlOIPP3mma3vc\nltTQihNu/VpvdZ/awyGEIGuw3bJ5U+86BCMpcR5703JiXz+5x24HkvuGrglL7iUH2cM/auJW+P35\nA6vasrHudXaUFTs/DsuhfbfBkM9DrW0HRiR2o1sjsKbl4B++dmPofQ+DkEZVzCOUUkIpfSml9H7v\nv4fTOLgoNhoW9hYzMHUSW+7Yy4rRtMHGWvH3zEtVMXHNswI/Kz2IZCuGJ874UAQeuMPJ04WYWvat\nhi12wSXlO192CK89MS+sGH5D1LwyUbntQq+WwHHoGsF33H8Qn3xuBV+6uI5jC6VEzcT4eLwo/B7c\nTLE3LAeX1+tYLGdxcDbfUcvesh3U2w5mYx5+3/Gyg5j32huY0mQl7ufOJ1Dsy9st/KePPIcPfPly\n5L/7LWj9z7WcMwN93uuWE6u2OfzakG2YQcn1qIqJV+xJPXarY1V5h+ezf/OLlgBED1sPv3+ZB/am\nLSn2znJHx6WRydM45Oqgeiu+F7s4ngjFTinFz7//Sfzon54SewVGyQTuPGWVEL1mPophBjE3yCD9\nYuSOi4DnsSe0YriHOV/KYLNhCXXoK3bfiqGUBnaeAv4mpeWIwM5umsFucFazzRSG61I25CFrYLbA\nAmbLdljydEArBgC+8+UHYbsUT1/Z6kicdqOQMURDrDDcY58tmGL04ZnlKhYrWRyYzWNluxXwfPnn\nHBcEc6aOH3zVEQD+Ss/QiEiozuRNZKRAHwXfnt8tyR01jagkVXkA3tSeBAqcq9iZPldq3V6LNb2K\nqCNPUbGHA/vdns/+zS/aByB62HrLdgMPQrGpq8WsGF0jqOSMjp2nlhO9QSmOXMiKiath51RyZofH\n/p5HzglbL7wZcRRMXGDntctZM35qC3/yxwX2QeYVylONAGbFyI2Hkvzsvpmc1+HRV+aAX5621bDE\n7yY3+Y9V7E27byuGQwgRD0qeOCpKHSU3G9ZQVgzAfF++lZ8PVu5FPqN33aAkKzW+vL+wVsdSJYeD\nXsWLPACFb0SbkapHovjxN9yBv/mJ12CxzB6yhq6JmzZn6ijljNhyx4veZKZuZalRDbVKnhUj92/h\nVVtx8GA71+N3SkJ41SaT1GPv3eKjU3z84KuP4C9+5AHcsVACIZ2BvduDkL/eWo0lxAkhotyRCyhW\nxz64FbPZ6FxhRBHuFPv0lU38xsPPiOt9HInViQrsrjffkvWFiFfsfGnbzWMHBlPs/D1lKwZAorad\n3IrZV2GBhz/JRfJ0lit2WwT7vLQxI96Ksfq2YmRyJkueyRYWD4JbDWuo5Cnnu1/O9q0dTajYixm9\na1XMet2CqZPAA8hxKbNivFJO2Y7h1tdcD9vC0DVRBw4wxV6VA3tIXYfhij1qVQVEt8At59jgbv5v\nzFbr/ZDmwS4VK8YI5llkkir2JOWO4UA5kzfx6uPz0DSCgql3lDt2y0kATLxteEIP8M+p3CtG7zt5\nqolrbq3Wwt5S74dmuKHg45c24FLg330r24DPBZzr0pG1952owM4sCqbScj0UO79ASr3GWvVtxXhK\nmlfFeBdcEjvGV+wsQHPVyVcXvE/4VsMS3ysvBctZttwML/N5n+tBrRjAX4rXpGoiHjA36sMrdgB4\n+9fdhu9/8HZ8/Ylk5a75DGuJHLXNnG8jJ4QEVipLlRwOzbINV3ICldc7z+b7U7eGTgIjCsPb2cNc\nEoE9ukc/D1Ty0AruGXNlxxR778+Si4s0Ajt/rai9IckVe/+BXaaYNTqavvmDrKOSpxbWan5g58JD\n3qBk9umxFzJ+G+61Wls0qIujnDOx3fTn7q5st0CIPzqTXy9PXdnEHf/mYXzi2eW+jmkQJiqwb0iV\nEKwHdIxibwbH4kUxiGIP17byOtkkTZC4GuKWy4ZIktrIGhqKWQMZQ8NW0xKNiHJS8oYQgsVKNrAR\nB2A3VNtxEy3fu5Hzdtz58zgNkWhcr1uwXTp0YJ8pmPi173iJ8MR7ITofRnzOck36jPR7L1Zy2DeT\nAyHRir3fIChP38l7Vkzc0vqCF9hvVtuR6kye38nhq0qu7LaayRQ7fzjMpmjFRJ1r5nEPV+7IxEd8\nHijqoRlnxVRbjsi5AZ1ev+1Eb1CKQ04ir1b90uo4KnlWfsmPfWW7hb3FjDguf5dsbxchLSYqsMs1\nq70Ue60dHIsXRT9TlLaazI7gH7oodxSKPXlg58qc+75ytz+2irDFyiBcQ7tQ6tx9uiW2ag+u3LKG\nhqbliouzmPUtDm79DLpBaVB4RUKUHbPuKXYg2EZhsZxFxtCwWM4GArvvsfd3juTAkDd1lHso9otr\ndWiE2UJrEUMkogJV2ZvyVW3ZsB32GSTz2D0rJoXkaXgvg0zTcrqOxQP8fEHc/djy5rjGKfbwRi35\neMIblAC/KoY3kQs/YAatY+ebBLdbdqLAvhAqaljZbmKhnIOpa8iZfrKd2zVJ+zkNw0QFdr8SItPT\nY2d9YuJPYK85ojJve9cj+INPnPE9djPosdsJrBhfsbPAzh9U9ZZfrz6TN7DVsLrueuOblGT8C2Y4\nxd6ynYAVEx5GPUgTsGHgieOokkc2NYgdn3yj8IZiB2fzAStmo8GqJ8oJyghl5HK5XEbraBkr02g7\nWNluiaRZlB3TLXkKsEDFXzuRYk+x3JFXnQyi2JN47EnER3ijFn9vIHjt5UzN219gBR7whs46ZcpN\nwPpV7PkMex8uCvYk8Nh5zozvAl7ZbolgX8r6FTNbUnXVTjNZgb3h1y7nTC22V0yt1X0sHkdMP0nQ\nL+bqRgNPX9kM+K2Ab8UkU+zse/gGqw1JsXMVwlcR4ZUBZ6Gc7UjM8Qtm0KoY9j4as2JERztD3IQr\nVXbBDmvF9EvUdCHO9a2mCOI5Uxc3Pi8JPThXCCj2tZqFmbzZ1zBuILhKyfdInl5aZzbMycOsV0tU\nkjuqUyL/7Leatv+QTuKxm+lZMb0Ue1xLgSRVMf4gmJi+K9nOiqMoxc46Yuq4sdWC5VDsKfrnirUQ\n9qpinM7ReL3g5+GyJwqSKHYu1K7Jgd3b81CRhAC3fYexTJMyUYGd7zKbzXsee8yFVI0Zi8dJOv3E\nctisxgur9Y7kaSZUOxsHD9bFrI5KzghsROJBjCd0G10aQS2Wc9ioW4HfPclN04u8SJ76ZaK6RlDO\nGSJADVsV0y/d5p5WWzY2G5Zo5AUwFVTOGsLSOjibx7XNhki8Xt1o4ECXplhxyL1GeLljtzp2Xur4\ndV5P9KjKGF+B+p8rV+fVlt9HPslnyVV2GlZMLiawp6HYqwn2lRQjAnuUYgeY8ueJavnBljX0kBXT\nr2Jnx3fZe0jvLfVOnvL9J9c3G6CUYqUqKfac4edOGmweQJI9CsMyUYF9o94GISwg91Ls1ZixeJyk\n/WJ4YLmwVvctkpAV04/Hnjd1zBYywoqRB4IwxW7j06dvImtogeAF+H7eqjQiT7TsHboqRi539Jf5\ny2Py2AtdrJirnhI/KPWUr+RNLFT8m/DgbA6WQ0U+4spGQ9S394Mp9YwxdQ2ljIG2NBtVhidOYxW7\n1T15Wm1afbVfFh57qoo9+Hu5LkXbdmM9dv7Aj/PYw73YoyhmO8sdudoNbxQqZnWhqvdIv788f3WQ\n5Ck/D9zG25NAsedMHXMFE9c2m9hsWLAcKlkxRiB5OsiqcRAmK7A32InRNSI84W5Ue5RWAcl7svOA\n3LZd0QMkXMeezGPny3B2IXArRvbYKzkDN7aa+OsvX8Z3vfxQhx/Hl3iyGhSKfSgrRkfTdvzkqXcj\nzeRNX7GP0Yr54rk14WFyi+WgpMAPzuZxdK9fH8+D/uV1pqKurDdwcNbvQZ8U7rFzRVsSNdSdqv3S\nWh2lrIH9MzmUc0ZH9RLQq8pDVuzJPfZetflJEFUxoYcoD5Jxit3Qmecdp9jDvdijYINVguf1pvdg\nni8HA2wpa+Ca15p5TrZidE2UlEbNPO1F2GNPYsUArM/T9c2muC+5JVgOWDGDbyLsl503e1Lke19x\nm2i3yas4uiFXmnSDB8nzN2vAXd2/T77Yn7u+DV0jYkcbVwT9WDFZQ8NMISNK8Hg3P4AFZ75CeOdr\nj3S8BveVr282AG8jzVaCm6YXfAVUa9koZHTRgW82nxEDh8cV2J+9to13ffw0vufkbfiP3/USodjl\n1czvfu/9kG9hHsSvbDRwZG8BDcsJTI1KCv98uZKTg/Bc6Ka/uFbH7XsKrCw1IhcCRA+tyBgasgbb\n4ep77L0/y9m8CVMnfVf6RCEUe0gs+RuE4u2DjK4l8th717GzfQv8+uOiYm+onryYNURDPXnnbdbU\n0BKKfbCWAgATBIZGEq+C98/kcH2rKY43Mnk65CbCfpgoxf6iAzOip0QSxR7n5wHAbXsKuHtfGR/8\nytXY75MrBZ69vo28qYvlFL9Bu/Vkf/TsKv7aawjVshzkTDawYDZvikZW9bbf9Ikr9DfctRDoPsjh\n044urfmJwe3m8N5d1tDRbDuohfpjzOTNwIDnUcKP47995iwcl+K0N17vinfT8W3/AFsyy4GW++lX\n1hu+wh8gsPM6dr5CK4ua807FzgM7wHIh3Tz2qKEVZc+776d09Z8+cDv+54+9umfQTYKoigkp9qbY\nIBT/2WfN+BGRSX4vfr/KyfKb1VZg7B1HfkDIgT0jjarsNmgjDtmKmStmxAOmF/tmcri+2RnYy7LH\nnnDjWRpMVGCX4Yq9W4+Wasy8U5nvfvkhPHFpQ8xejCI8yFjO0Psee/Rx/MnnzuO3PvqceB15+Sy3\nFCh4njb3C9/52qORrzdTMFHJGbiw5reF5b3Yh/HuuBUTriaS1WB2xB47D6bVlo2MruHMShWUUlzd\naGDfTC62c185x87T1Y2G8EvTUex+olPGdSkurdVxuzc/llUvRVsxUYGYe7FbDTaMIklZZjln4n6p\n/cEwdOsV059i7+2xx92T/B6Qk+Vy6aAMX+FqJGhBZqXB2rbTf/KUi4kb283ENgwA7K/ksFpri6Tr\nQsiKoZS1Q1GBvQdcYURdTL3G4sl8+8sOQCPABx6PbrMKAM2QiuE+HOC3d7Xc6It6q2mJAC5v9Fgo\nZ7HZsLBZZw2/+IX61pfux3t+6CRe22XCC8Am4FyUFHsaSiBnsi6VW00rYGHJHr85JiummNHx0OuP\nYaNuYbXWTpwI5SWPPMl2aACP3Qh57NwiWa8HNx+t1tpo2a44rsUuQ1FY6WDneeTb0sPDKEZFxqsB\n3ynFzucPxz2MZZuLs7LdEu2SA9+b81e48muyqhiHtaKg/W/a4w9wSpMlTjm8MubpK1vIGpp4MJc8\ny6jedhL3AEqDiQ3suZjA3qsXu8xiOYfX37mAD3z5SmRPEsBX7LxXdz5KsXe5qLcaNhqWg6bloGm5\nQoW+yBss8Og5Nj1GBLGsgTfdsxSrvm/fU8DFVV+xhwcYDAI/n2u1duC8yaV0oy53NL1BDD/5xhN4\nxVFWQnhmuYqrG81kgd3bpHRlo4Fy1hiofph7tPwzP+KN9OOToDirNS/J5wWhxUoWTcvtKI3sVjrI\nt9MzH3Y0N78MIURURsn0pdhj8kysx3/8a3BxIyemb1bbkYqdPwTCnS0zBnvA8KqxPX1WDOUk0Zak\n1JHD24Q8eXkDi5WsuF82vEQAAB31SURBVH9FxZNns42ihh2Y4MAuNkVE1N2KZV/CRMV3vfwQrm42\n8QVpRJcMXxrevY/tKIwM7F2sGF5xs+k19uLHfd8htoT+3AvsPZM8hDi37y3g8npD9CLZStheNA4+\nXHm12g6sdGTFPmqPHQA+9rNfj3/xhjtw3BvI8PyNbVzfanaUgUZxaC7vKfY6Ds7lB7KquBXDFWsl\nZ2JfJYfT3ixYzlrVn70JQPj/4fa9LTt6ez7vQTNM++VhkYdMcBIrdkOPnWhWt3r3NudWDFfslNLA\nZh8ZEdiLnYG9ZbtiRRX+917I93Y/VgxX7Fc3m4HjFZv8tlto2+5Idp0CExzYYxV7u7efJ/ON9yzC\n0Ag+c+Zm5L/zi/3ufeXAewO+FWPHWDEAW7o3pSHYe4oZHJrLi4dJX4F9TwG2S0V1SJqK/Wa1FdgU\nJW9XH0dg58H4wEwOhYyOz565CceliRKhB2ZzqLZsPHNteyB/HehMngLAiaWSqBTirHp9YXibV38o\nSqhhmxWt2MsisI+uciIM7/Apk1ixS/XjUchzgrvB71feg7/WZpbKfJTHLhR78LrPeoqd9+mRd6Um\nQT7GQawYAIEVBrdkeAJfWTE94Mo3aqdckl1uMoWMgRcfnMGp82uR/87f4y4vsMs3uRlqFSpDKRUb\nTjbqVkczpfsOzeJZb6ZokhFcnMOiMoYlatJY4skPSvm8VcZoxcgQQnDHQgmfPcMehEkUu1zyOMjm\nJKCzjh0Aji+WcGa5GrDu/EDiBfZKdO/8bsnTsmzFjEmx87YSMq2I4dtRlLJGbAvshmX3nONaDFXF\n3OQVJhGKna9QI60YR1LsfVoxhq6J6zxJL3ZOKWuIY5IDO3cNuAhTydMexCn2ah8eO+cVR+bwxKXN\nyAcFTyjx5k6FiMAeZcXU2o6otWWB3Q0saV9yaEb8OckILg6vvOA7HZkVk45iB9A1eToOxS5zfLEk\nPttkyVP/ew7N9Z84BfwVmazkTiyW0bCcQC+a1RrbFc0DyUIXK6Zb8pQ3FxuXxw4g0mOXN9XFsX8m\nJ4JXFHLbjG6Ek6d813BcVUyHFeNtUFqThlz3C79H+7FiAL9nzELJV+882PPKLGXF9CBWsbd6b4YI\nc/LIHrQdF09f2ez4N27FHF8sQSPRVkxUSwF5R+tGyIoBgJdKgb1XYklm/0wepk5wca0O23FRazsp\nWDH+pRBInoZqhMcJ99kBJOr7Igf/QWrYgc7kKcCsGACBEtm1WguzUoVGJWdgbzGDZ0KDjFu2Gxkk\nS1kTjstaIIwqwRYmymNPqtgPzuWxHJozK5PEihE7jaW+5gBiq2K6KvYan4Xa/33h26XJk6cA230K\n+Ks1wH9Y+VaMSp7G4jct6h5Q+/lQeX+Px86vd/wbT3rmTB1vuGsRLz3oB2R/glLncchL0w0veSpb\nMS85OAOez+tHsesawaG5Ai6u1v02rylZMQCCdey7SLHf4U2kmSuYic7XfCkjjnlQj52XOwY8du8B\nIydQ2bQdP8gQQvCa4/P49OmbgZLHlt2t3JH9PpZDJ1KxR82ZlWlYvRW7XxXDjuFmjGIvdfXYWROw\ntXobcwVzoLJR/gDqV+3vr3DFLnvs7PiUFZMQf0NFp0JY3mKjqfrxyPaWsji2UIz02ZttX2m/95+9\nAv/sNf7mIZ5ci7Ji5MDOkqduYCJSOWfimFc+149iB9iu2YtrdZz2VOMgS04Z+caVg2Yxo4vgNuom\nYGG4Yk+qvgkhIuAM6rGH69gBtopZKGcDCVQ2bScYgF57Yh43qy2RRwG6j5mTV5fj89gjkqd9KHYg\nOLVKpt52AoPZo9A0gkJGDyh2jURf20fni3jdiXm80iuD5fC2vevSyLx+4Z/1fB/xA/ATqFEeOz8v\nyorpQdborthXqi3sKWT6DkSvOLwHpy6sd9Sz12OWkXFWzJa07XwzInkK+GWP/eQDAJZAvbBaw+//\n42nsLWbwjfcs9fXzYaL6gwMsOPKLsd+J72lzeG8BhkZwYCZ5kD44m0fe1Ad+8EVZMQBT7acDVky7\n4z1ed4JtMvvM6RXxtW69zQMJ67FVxXQmT5Mq9vCc2Y16WzRtA5JZMYDXurctjZgrZSM3NRWzBv77\nOx8Qc0U5GYNttFuttvsudeQUMvpANs7xxRJMnQSEh+49rG565bDDliUnZWIDey/FHrV868XJI3PY\nbFg4sxIsZWtY3S9KXSMgJN6KyZmaXxUTKnV723378eCxPbFDt6M4vLeAraaNR87cxL94wx19PxjC\nyA+c8GvNeL06RtFuNA5T1/DPX3ME33b/gcQ/8/o75/GmexYHPnaRPM10BvYzy1Vhs6zV2h3TdvbP\n5HFisYTPnPbLaJnHHr3zlDPOOvZuVTG9bDg+Z/ayp0x/+QNP4//6sy8BYNVh9bbd04oB2ApRtmKi\n/PU4+Mrixnaz781JnHxGx1wheZ8Yzltfsh+f+tff0HHMPJjnTC2Vvj5JmKjujjK9FPsggf0V3oCE\nz565iTuX/AZcTanHSxhCWJ/uKCuGe/237yngZrUF26UdD4g33r2EN97dv9q+zSt53FfJ4fsfPNz3\nz4cJVsUEj3Emb2Jlq7Oh1Tj45bfe29f3P/T6O4Z6Pz6BJ/y5HV8qo9qycW2ziX2VHNbr0YOPX3ti\nHn/x6EVxDbE69njFPipVFyYXmTx1YeokthUAwAL/UjknFPuXL66Lbpttx4VLOx+OUcjDNrr1iYmD\nB/Zrm028+o7ubTnimCtkBhrKomkksgy3lDVwA62R5k6mUrGvbDUHCuyH9xbwogMV/I/HLgUSXo1Q\nNUsYUyNdrBg/sPOxWb2WtEm5a6kMQoCf/sYTqbxmNysGYG0Fxp04HRf+ztNOxQ4Ap5er2GhYcLv0\nFnn9iQW0bBePnV8DpbRn8hQY3SaWMFHDa3oNspY5OJfHlY061mptXNtsinYK3aaBRVGUhoV323Ua\nhzzNqd/NSZxfedu9+C/f9/KBfjaKkvd5jspfB1IK7ISQ9xJClgkhT6fxeknoVhXDR1PJLV2TQgjB\nDzx4GM9e38apC351TKNHDa5paF2sGNb4aG/R7/TXa2t2Uo7MF/HIL7wR73jFbam8XrfkKcBqhdN6\nIE0aRsTOU0AK7De2seb1iYkK7A8c2wNDI/jC2VXYLoVLoxORcmAfZQCQ4eWOwSqe+LF4MgdnWQuH\nr15lJcM1r6shb8mRyGPP6Ki12c/drLY7Bmz0Qj63gyZPlyo5sVckDXjOZJQWW1oy7E8AvCWl10oE\nr6kOe4IbdTaaanEAxQ4A33b/AZRzBv7sCxfE1xpWdO0xh1kx0Yq9kjMwWzCFVZNmgDw4O1j/kyii\nJvpw/uUbT+C3335fKu8zaYTb9nL2lrLYU8zgzHJVNJwKV8UA7CG5t5TB8lYrcjAzp5gdv2KP6pja\na5C1zMG5PK5tNPGUtxfEpUx4icCeULHXW6wTYttxB1bswPCVYmkhBtWP0GJLJbBTSj8NIHo//g6h\naUQ0/JGJ262WhELGwHe//BAefuqaqKNtxiRPAfaQ6eaxV/JmYJPPblW+hBAR3MMe+9H5Il51x95x\nHNbYuW2ugIyuRZZYHvcqY8LtBMLMFTJY99ozA9GK3dQ1sZpL2rwubfy5p75Y6lex2y7FJ5/1q4C2\nW5Z4vSR7D3iXy5UqW+H2ex9ndP/aHbQqJm14YJ84K2ZcsGEbQcXOt3APqtgB4PsfvB2WQ/HhJ9hk\npXrbjg3sht7FYxeB3f9ARzGhfFC4ouo1BPxW4t4DFTzzq2+JrIO/c6mE0ze2OxqAhZktsGlZfmCP\nvgbKORPlHj3Ld5Ioe7NlxQ+yluEPv8curIH/CrWWIxR7Uo+91rKxss3Oab+KXX5oDloVkza84mkS\nrZieEEIeIoScIoScWllZ6f0DCWDj8cKKfbAnvcwdCyVkDE0kPBvtHsnTrlYM67oo9zTfrYodYCWP\n8rxTBaNboD2xWMZW08az11nbgG6eLlPsbdFiupsCZj3jx2PDAP4AmUZAsTuJFfsh7+FHKXsgAqwh\nHx9QneTaL2Z01C0Hf/OVKwD86q+k7Eorhnvs01gVQyl9N6X0JKX05MLCQiqvmTW0jn7sQrFX+k+e\ncgghmCuYokNcM5HHHr3ztJI3QlbM7l0k5Uxt6Hr4WwmeQP3C2TWUc0bXyqHZQkY0gQO6K/ZSzhhb\nqSPg72UIWDFW9E7ZKGS76pVHmHVXbdl9V8VQCrzvsUv48TfcMRWBvaysmP6IVOzbLeRNva82uFFw\nX9R2XLQdN74qJsaKmQlZMbtasadw3m4ljkvNwOI6Ac4VTGw0LDG0opsCvmOhFGh0Nmp4uwtZsTft\n7ns4whQyhgimDxxje0JqLVu8XtLADrBuqz/75juTH7wHfwhlDC3R+42CsqiKGd1DO5V3IoT8JYA3\nAJgnhFwG8G8ppe9J47XjiNoCvbzdCoymGhTuiza9B0ecNx5lxTguxXbLs2ImJLBnTX1s/u4kslDK\nYiZvYrNhxarDuUIGjktFf/FuCvh33n4foudwjYZhFTvAEqiUUvGAqrbsvqpiXnb7LB48tge/+733\ni3YO/cAV+55CZuw7pTnjsGJSCeyU0u9L43X6JWvoQgVxBtnUEMVcIYPTy1WxjMz1Uux28Jbkwz4q\neTPgve5mK2Z/JQeHjjO0TBaEEJxYLOHUhfXYFq+8OuPGFsvZdLNixp3b4IG3OaBiB4BvvW8/NhuW\nsB9kKyZJ4cCLDszgfQ+9qp/DDsAfQrulIgbwA/pMYcIC+7jImVrHnMXl7aaYdDQMs4UM1mttcZH3\nUuxVOzi0mO86reQM5Eyd5QNsd1dXxfzW21867kOYOE4sscDey4oBgOtb6W5SSxt+XOGqmH4UO2/h\nwNsC1Fq2eL1+WlMPCn9oDrrrdCd48Nhe/Mrb7hUtS0bB7rzCErKzip35orzTXL9WDO8TwxMmXLXv\nZiumnDOHnsR0q3F8kYmIcAMwGZ4851VWo2oE1S/ciuEKG/CGbw9wzRYyOgjxrBjLRsbQRmLzcStm\n0F2nO0HG0PDO1x4dadvriQ7sYcXetBxsNe2hKmI43BflVTa8FCyKKCuGd3bk5WvcZ9/NgV3RP3d6\nCdS4mmmu2H0rZnfedsKKkcRSs0/FziGEoJRhm42aCcbipQXfkb5bKmLGxURbMWHFvhIz/LZfuEd3\nbZN1q8ub3U9VlGL3rRi/AVBGH41qUYyOFx2YwUzeFHXbUXD1yPuTJ60LHzVcdHDF7ro0tmV1L4pZ\nQ+SaRmVB8nO7mxT7OJjowB5W7Ms8sFfSsWIA4Ko36isuo5/RNVhuKLA32AXNEyZzhcyuvaEVg7On\nmMET//abYr+nkjdBCHDDW/3t1lUbL3XlVSx1L780aIuDUo4NzSCEJKqISYNCxsCvf+eL8fV3prNX\nZlKZ6MCeNYKDAdJU7L4vyhV7j5YCYStGSp4CbObmMLthFZOLrrEpVBt1dk3sVivG0DVkDU20zeVq\ne9BNa6wFrwPDmyI0Kv7PB4afTzDpTHZgNzVRZw74HuZiioqdJ7wGSZ5qxO+78q/efCd+9PXHhj4u\nxWQy5+0+BXwfeDdSzvn90Pn/w90+k1LK6qg2LWQNHYUYK1ORPrv3CktAwTTQtl0xbOP8ag2FjJ5a\nHTvgTxfPxSZPNbTDHnvDQjnnT0kvZg0spZDUVUwmPHme3QUjBuOQfXFesjhoU7hS1mBNwCwndh+I\nIn0mOrAf9prhX1itAwDOrtRwdL6Yyo3DfdFkip3AdsJWjD22gQmK3ccklLsCPBiHAvtQVoyNRttG\nYZf/3tPGRAd2vm35jDct/tzNWsfU8kHhvmiS6S9RVsx20xp4CauYPmTFvpuRR9Px/w/amKzsvVZ9\nhOWOCsbuvsp6cMdCCYQAp29U0bIdXF6v4+h8MbXX5yoro2uxfStMXYPt0o45qepiVnD4tbTbK6PK\nEYF9GMVe81oKjKoqRsHY3VdZD/IZHQdn8zizUsWltTpcChxLMbD7m4riTxPf7Sa37u3V6ldxazEn\nFPvuviaKkVbM4HXstkux2bCUyBkxEx3YAWbHnFmu4oWVGgCkqtj5bsJeasPwEqSyHdNoD7YVWzGd\nzAqPfXffckErxqtjH1CxcwvHdumu7pE0jezuqywBxxdKeGGlKnz2owtpKnYvsPe4KHkPCDmwNy21\n/FT4CCtmlyt2udyx1rKhkcF3jcrVNHk1bnGkTHxgP7FUQtt28ZnTK5gvZVPteTyXsL+L6Vkxcskj\n24o98adXkRJzk5I8zRhoWi5sx0W1ZaOYNQauMpO9eWXFjJbdfZUlgFfGPHZ+PVV/HfD7xfS6KDM6\nu/DtgMeurBiFz6xQ7Lv7luPtA2otB9WWPVRll1xNo1avo2V3X2UJOL7A2qY6Lk3VXwf85Glvj73T\nihmmeZJi+pgrTkZ3z5KXKK22bdQ8xT4o8s+qe2G0THxgnymYmPd2mqbprwO+L9rTYzeCgd11qaqK\nUQSYmxDFzoNxtWkLK2ZQSsqKGRu7+ypLyPFFFtDTtmKS9lDnVkzbawTGB2yr5aeCkzN15Ext1ydP\nS9JIu1rLFgp+mNcC1L0waqYisJ/wptgcG5di96pibK91L+84mdvl6kwxWt7+dbfh9bu8nWwwsDtD\neexy/fsoxuIpfKbibL/hrgU8cXkDt+/ZocDey2MPlTs2rORT2RW3Dr/6HS8e9yH0xE+eDm/FBMod\nlS05UqYisL/pniW86Z6l1F83afLUDFkxPLArj10xafBgXPUC+zCKXdMIihkdNdUrZuQoryCGnKnj\nB191GN9w12Ls92XCij1B4zCFYjfCSxSrzeGrYgA/GatWr6NlKhT7TvIfvr338tno5rGrwK6YMHgg\nXqu1Ybt06A6lpZyB5e2WUuwjRin2FAhbMU1LVcUoJhNT15AxNFz3ppEVh7yG+YMht8urgaYNFdhT\noMOKsZQVo5hcyllDjJksDdmio5Q1kDM1MUlMMRpUYE+BcLmjnzxVp1cxeRTlwD5EHTt/LVXqOHpS\niTyEkLcQQp4jhJwhhPxiGq85SRieFWNxK6atPHbF5FLKGrix1QIw+JANznwpKxqgKUbH0I9SQogO\n4A8AvBnAZQCPEUI+RCn92rCvPSlwK4Z3d2zayopRTC6lrIHNhgVg+MD+c990J7a94diK0ZGGYn8l\ngDOU0rOU0jaA9wH49hRed2II92MX5Y4qeaqYQEpSV8Zhq2LmS9nUm/MpepNGYD8I4JL098ve124Z\neBMw3rZXeOyqEkAxgcgqXQ1kn0xGlt0jhDxECDlFCDm1srIyqrcdCXw0XluqiskYqhJAMZnICdNh\nrRjFeEgjsF8BcJv090Pe1wJQSt9NKT1JKT25sLC7GyH1S9iKaVmu8tcVE4us0oetY1eMhzQC+2MA\nThBCjhJCMgDeAeBDKbzuxKBrBLpGAh67CuyKSYWr9JypiV3Visli6HUWpdQmhPwkgI8C0AG8l1L6\n1aGPbMIwdRLw2FUNu2JS4Ypd+euTSyqfHKX0YQAPp/Fak4qpaQGPXdWwKyYVFdgnHyUrU8I0NGHF\nNC1HlToqJhZuxajE6eSiAntKmDrxd56qQdaKCYbXsavAPrmowJ4ShqbBcpUVo5h8lBUz+ajAnhIZ\nQ4PFk6eqKkYxwZSUFTPxqMCeEsyK4R67qxS7YmJRin3yUYE9JUxdC0xQymfUqVVMJn5gV+JkUlHR\nJyUMXUPLljx21SdGMaEUswYyhoY9xey4D0UxIGqtlRKVnIGthgVKKRqq3FExwWQMDe//sVeprowT\njFLsKbFUyeHGVgttxwWlasiGYrJ56aFZlIcci6cYHyqwp8RSJYuVagu1lpqepFAoxosK7Cmxr5KD\n41JcWW8AUNOTFArF+FCBPSUWKzkAwPnVGgCoqhiFQjE2VPRJiSUvsF9cqwNQil2hUIwPFdhTYqnC\nSsPO3WSKPasCu0KhGBMqsKfEQikLQoAL3IpRgV2hUIwJFdhTwtA1zJeyOL+qrBiFQjFeVGBPkaVK\nFivbLQBQG5QUCsXYUIE9RZbKOfFn1VJAoVCMCxXYU2RpRgrsqtxRoVCMCRV9UkRW7MpjVygU40IF\n9hThJY+AaimgUCjGhwrsKcI3KRkagamrU6tQKMaDij4pwgO7smEUCsU4UYE9RbgVk1OljgqFYoyo\nwJ4ic4UMTJ0oxa5QKMaKCuwpomkEi+UccqY6rQqFYnyo0Xgps1jJwnHpuA9DoVDcwgwV2Akhbwfw\n7wDcA+CVlNJTaRzUJPPjbzgO23HHfRgKheIWZljF/jSA7wLwxykcy1Tw5nuXxn0ICoXiFmeowE4p\nfQYACCHpHI1CoVAohmZkWT5CyEOEkFOEkFMrKyujeluFQqG45eip2Akh/whgX8Q//TKl9G+SvhGl\n9N0A3g0AJ0+eVNlFhUKh2CF6BnZK6TeO4kAUCoVCkQ6q4FqhUCimjKECOyHkOwkhlwG8CsDfEkI+\nms5hKRQKhWJQhq2K+QCAD6R0LAqFQqFIAWXFKBQKxZRBKB19gQohZAXAhQF/fB7AzRQPZydQx5gO\n6hiHZ7cfH6COsR8OU0oXen3TWAL7MBBCTlFKT477OOJQx5gO6hiHZ7cfH6COcSdQVoxCoVBMGSqw\nKxQKxZQxiYH93eM+gASoY0wHdYzDs9uPD1DHmDoT57ErFAqFIp5JVOwKhUKhiGGiAjsh5C2EkOcI\nIWcIIb+4C47nNkLIJwghXyOEfJUQ8tPe1/cQQv6BEHLa+//cLjhWnRDyOCHkw97fjxJCHvXO5f8g\nhGTGfHyzhJD3E0KeJYQ8Qwh51W47j4SQf+V9zk8TQv6SEJIb93kkhLyXELJMCHla+lrkeSOMd3nH\n+iQh5OVjPMbf8j7rJwkhHyCEzEr/9kveMT5HCPnmcR2j9G8/RwihhJB57+9jOY/9MDGBnRCiA/gD\nAN8C4F4A30cIuXe8RwUbwM9RSu8F8CCAn/CO6RcBfIxSegLAx7y/j5ufBvCM9PffBPC7lNLjANYB\nvHMsR+Xz+wA+Qim9G8B9YMe6a84jIeQggJ8CcJJS+mIAOoB3YPzn8U8AvCX0tW7n7VsAnPD+ewjA\nfx3jMf4DgBdTSl8K4HkAvwQA3v3zDgAv8n7mD717fxzHCELIbQC+CcBF6cvjOo/JoZROxH9g/Wg+\nKv39lwD80riPK3SMfwPgzQCeA7Df+9p+AM+N+bgOgd3gbwTwYQAEbLOFEXVux3B8MwDOwcv5SF/f\nNecRwEEAlwDsAWvF8WEA37wbziOAIwCe7nXewCadfV/U9436GEP/9p0A/vz/b+9sXqKKwjD+e6ES\ntEVWVIaBFtE2XRW1CGpRIrppEQgZ9Q+0CkoI2kfUImpRtAgpyCSGIII+1lZGZvRBRkIjmm4yqI3B\n0+KcwUka0haeM8P7gwvnnnMXD8/M+55733Nmbmz/EdfAQ2B3Ko3AAOFGYxxYn9rHxR5Vc8fOfGCV\nKMa+LDCzFqANGAI2SpqMQ1NA6vflXQROAaWXsa4Dvkn6Fc9Te9kKzAA3Yrnompk1kJGPkiaA84Q7\nt0lgFhgmLx9LVPIt1xg6DjyI7Ww0mlk3MCFpZMFQNhorUU2JPVvMbDVwFzgp6Xv5mMKUnmzrkZl1\nAtOShlNpWAQrgHbgiqQ24AcLyi4Z+NgIdBMmoc1AA395dM+N1L79CzPrI5Q0+1NrKcfM6oEzwNnU\nWv6HakrsE8CWsvPm2JcUM1tJSOr9kgZj91cza4rjTcB0Kn3AHqDLzMaB24RyzCVgjZmV/t0ztZdF\noChpKJ4PEBJ9Tj4eAD5LmpE0BwwSvM3JxxKVfMsqhszsGNAJ9MQJCPLRuI0wiY/E2GkGXprZJvLR\nWJFqSuzPge1xF8IqwgJLIaUgMzPgOvBO0oWyoQLQG9u9hNp7EiSdltQsqYXg2RNJPcBT4HC8LLXG\nKeCLme2IXfuBt2TkI6EEs8vM6uPnXtKYjY9lVPKtAByNuzp2AbNlJZtlxcwOEsqDXZJ+lg0VgCNm\nVmdmrYQFymfLrU/SqKQNklpi7BSB9vhdzcbHiqQu8i9xcaODsIL+ifDO1dR69hIec18Dr+LRQahh\nPwY+Ao+Atam1Rr37gPuxvZUQMGPAHaAusbadwIvo5T2gMTcfgXPAe+ANcBOoS+0jcItQ858jJJ8T\nlXwjLJpfjvEzStjhk0rjGKFOXYqbq2XX90WNH4BDqTQuGB9nfvE0iY9LOfyXp47jODVGNZViHMdx\nnEXgid1xHKfG8MTuOI5TY3hidxzHqTE8sTuO49QYntgdx3FqDE/sjuM4NYYndsdxnBrjN3H3fxft\nwJ1zAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cdbfe48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def gen_ar1(nobs, alpha, beta, sigma):\n",
    "    y = nd.empty((nobs))\n",
    "    ylag = nd.empty((nobs))\n",
    "    epsilon = nd.random_normal(0, sigma, shape=(nobs)) # innovations\n",
    "    y[0] = alpha + epsilon[0] #initial value\n",
    "    ylag[0] = 0\n",
    "    for t in range(nobs-1):\n",
    "        y[t+1] = alpha + beta * y[t] + epsilon[t]\n",
    "        ylag[t+1] = y[t]\n",
    "    return y, ylag\n",
    "\n",
    "y, ylag = gen_ar1(smpl_length,1,0.5,1)\n",
    "plt.plot(y.asnumpy())\n",
    "\n",
    "# We use the first 100 observations for training\n",
    "ar_data = gluon.data.DataLoader(gluon.data.ArrayDataset(ylag[:train_length], y[:train_length]),\n",
    "                                batch_size=batch_size, shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0. Moving avg of MSE: 2.68369013701\n",
      "Epoch 10. Moving avg of MSE: 0.565846990103\n",
      "Epoch 20. Moving avg of MSE: 0.40341791049\n",
      "The type of \"params\" is a  <class 'mxnet.gluon.parameter.ParameterDict'>\n",
      "sequential1_batchnorm0_gamma \n",
      "[-0.33336928]\n",
      "<NDArray 1 @cpu(0)>\n",
      "sequential1_batchnorm0_beta \n",
      "[ 0.]\n",
      "<NDArray 1 @cpu(0)>\n",
      "sequential1_batchnorm0_running_mean \n",
      "[ 1.96725404]\n",
      "<NDArray 1 @cpu(0)>\n",
      "sequential1_batchnorm0_running_var \n",
      "[ 0.80071753]\n",
      "<NDArray 1 @cpu(0)>\n",
      "sequential1_dense0_weight \n",
      "[[-0.94211668]]\n",
      "<NDArray 1x1 @cpu(0)>\n",
      "sequential1_dense0_bias \n",
      "[ 1.92470396]\n",
      "<NDArray 1 @cpu(0)>\n"
     ]
    }
   ],
   "source": [
    "ar_ctx = mx.cpu()\n",
    "ar_net = gluon.nn.Sequential()\n",
    "\n",
    "with ar_net.name_scope():\n",
    "    ar_net.add(gluon.nn.BatchNorm(axis=1, center=False, scale=True))\n",
    "    ar_net.add(gluon.nn.Dense(1, in_units=1))\n",
    "    \n",
    "ar_net.collect_params().initialize(mx.init.Normal(sigma=1.), ctx=ar_ctx)\n",
    "\n",
    "square_loss = gluon.loss.L2Loss()\n",
    "trainer = gluon.Trainer(ar_net.collect_params(), 'sgd', {'learning_rate': 0.01})\n",
    "\n",
    "\n",
    "epochs = 30\n",
    "smoothing_constant = .01\n",
    "moving_loss = 0\n",
    "niter = 0\n",
    "loss_seq = []\n",
    "\n",
    "for e in range(epochs):\n",
    "    for i, (data, label) in enumerate(ar_data):\n",
    "        data = data.as_in_context(ar_ctx)\n",
    "        label = label.as_in_context(ar_ctx)\n",
    "        with autograd.record():\n",
    "            output = ar_net(data)\n",
    "            loss = square_loss(output, label)\n",
    "        loss.backward()\n",
    "        trainer.step(batch_size)\n",
    "        \n",
    "        ##########################\n",
    "        #  Keep a moving average of the losses\n",
    "        ##########################\n",
    "        niter +=1\n",
    "        curr_loss = nd.mean(loss).asscalar()\n",
    "        moving_loss = (1 - smoothing_constant) * moving_loss + (smoothing_constant) * curr_loss\n",
    "\n",
    "        # correct the bias from the moving averages\n",
    "        est_loss = moving_loss/(1-(1-smoothing_constant)**niter)\n",
    "        loss_seq.append(est_loss)\n",
    "    if e % 10 ==0:\n",
    "        print(\"Epoch %s. Moving avg of MSE: %s\" % (e, est_loss)) \n",
    "        \n",
    "        params = ar_net.collect_params() # this returns a ParameterDict\n",
    "\n",
    "print('The type of \"params\" is a ',type(params))\n",
    "\n",
    "# A ParameterDict is a dictionary of Parameter class objects\n",
    "# therefore, here is how we can read off the parameters from it.\n",
    "\n",
    "for param in params.values():\n",
    "    print(param.name,param.data())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forecasting with autoregressive models\n",
    "\n",
    "Say we have a sample to $T$ observations, from $t=1$ to $t=T$, and estimates for the parameters: $\\hat\\alpha$, $\\hat\\beta$, $\\hat\\sigma$. We can easily forecast observation $T+1$: $\\hat y_{T+1} = \\hat\\alpha + \\hat\\beta y_T$, but then we're out of observed data. What do we do now?\n",
    "\n",
    "We can forecast $y_{T+2}$ as $\\hat y_{T+2} = \\hat\\alpha + \\hat\\beta \\hat y_{T+1}$, and recursively forecast $y_{T+h}$ as $\\hat y_{T+h} = \\hat\\alpha + \\hat\\beta \\hat y_{T+h-1}$. This is a sensible thing to do, if our model is correct and some standard assumptions are met ensuring among other things that our estimator unbiased we have: $$E(\\hat y_{T+2}) = E(\\hat\\alpha) + E(\\hat\\beta) E(\\hat y_{T+1}) = \\alpha + \\beta y_{T+1} = E(y_{T+2}).$$\n",
    "\n",
    "So the expectation of our forecast at $T+2$ is equal to the expectation of the observation at $T+2$. Nonetheless we have added a source of uncertainty to the forecast: the right hand side lag is not a forecast and not an observation.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_ar1_forecasts(last_obs,npred):\n",
    "    fct = nd.zeros((npred,1))\n",
    "    for i in range(npred):\n",
    "        if i==0:\n",
    "            fct[i,:] = ar_net(last_obs)\n",
    "        else:\n",
    "            ypred = nd.reshape(fct[i-1],shape=(1,1))\n",
    "            fct[i,:] = ar_net(ypred)\n",
    "    return fct\n",
    "        \n",
    "last_obs = nd.reshape(y[train_length-1],shape=(1,1))    \n",
    "fct = gen_ar1_forecasts(last_obs,pred_length)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ce4ad30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit = ar_net(nd.reshape(ylag[:train_length],shape=(train_length,1)))\n",
    "plot_forecast(y,fit,fct)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean of the AR(1) process can easily be computed: \n",
    "\\begin{align*}\n",
    "E(y_t) &= \\alpha + \\beta E(y_{t-1}) + E(\\epsilon_t) \\\\\n",
    "\\mu &= \\alpha + \\beta \\mu \\\\\n",
    "\\mu &= \\frac{\\alpha}{1-\\beta} = \\frac{1}{1-0.5}=2.\n",
    "\\end{align*}\n",
    "\n",
    "Our forecast reverts to the estimated mean of the series, the dependence on past observations decays rapidly. \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forecast uncertainty\n",
    "\n",
    "For most useful applications of forecasting we need to know the uncertainty around the point forecast, ideally by having the forecast take the form of a distribution instead of a single point as has been the case thus far. In this section we are going to transform our AR(1) point forecast into a distribution in two way. First we are going to derive the analytical distribution, then we are going to generate an empirical distribution by simulation.\n",
    "\n",
    "#### Analytical forecast distribution\n",
    "Our AR(1) model is linear with Gaussian disturbances. Assuming for simplicity an initial value $y_0=0$, we can write observation $y_t$ as a sum of Gaussians random variable: \n",
    "\\begin{align*}\n",
    "y_t &= \\alpha + \\beta y_{t-1} + \\epsilon_t\\\\\n",
    "&= \\alpha + \\beta\\left(\\alpha + \\beta y_{t-2} + \\epsilon_{t-1} \\right) + \\epsilon_t \\\\\n",
    "&= ...\\\\\n",
    "&= \\frac{\\alpha}{1-\\beta} + \\sum_{\\tau=0}^t \\beta^{\\tau} \\epsilon_{t-\\tau}. \n",
    "\\end{align*}\n",
    "The above formula gives us the moments of the $y_t$:\n",
    "\\begin{align*}\n",
    "E(y_t) =  \\frac{\\alpha}{1-\\beta} = \\mu\\\\\n",
    "Var(y_t) = \\sum_{\\tau=0}^t \\beta^{\\tau} \\sigma^2 \\to \\frac{1}{1-\\beta} \\sigma^2\n",
    "\\end{align*}\n",
    "Since $y_t$ can be written as a sum of Gaussian innovations it is Gaussian, so we can write $y_t\\sim\\mathcal{N}(\\mu,\\frac{1}{1-\\beta} \\sigma^2)$. By extension the above argument also implies that our least squares estimates of the parameters $\\alpha$ and $\\beta$ are Gaussian.  \n",
    "\n",
    "\n",
    "Now define the forecast error at $t+h$ based on information up to $t$ as $\\hat\\epsilon_{t+h|t} = y_{t+h} - \\hat y_{t+h}$. Using a recursion as above, and noting $se()$ the standard deviation of the forecast error we can write:\n",
    "\\begin{align*}\n",
    "\\sigma_{p,1} = se\\left(\\hat\\epsilon_{t+1|t} \\right) &= \\hat\\sigma\\\\\n",
    "\\sigma_{p,2} = se\\left(\\hat\\epsilon_{t+2|t} \\right) &= \\hat\\sigma\\sqrt{(1+\\hat\\beta)}\\\\\n",
    "...&=...\\\\ \n",
    "\\sigma_{p,h} = se\\left(\\hat\\epsilon_{t+h|t} \\right) &= \\hat\\sigma\\sqrt{(1+\\sum_{\\tau=1}^{h-1}\\hat\\beta^\\tau)}\n",
    "\\end{align*}\n",
    "\n",
    "And so a 90% prediction interval for forecast at time $h$ is $\\hat y_{t+h}\\pm 1.65 \\sigma_{ph}$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# estimate sigma_{ph}\n",
    "residuals = y[:train_length]-fit\n",
    "sigma_hat = np.std(residuals.asnumpy())\n",
    "dense_weight = params[\"sequential1_dense0_weight\"].data().asnumpy()\n",
    "batchnorm_var = params[\"sequential1_batchnorm0_gamma\"].data().asnumpy()\n",
    "beta_hat = dense_weight*batchnorm_var\n",
    "\n",
    "sigph = sigma_hat * np.sqrt(np.cumsum([pow(beta_hat,2*h) for h in range(pred_length)]))\n",
    "sigph = np.reshape(sigph,(pred_length,1))\n",
    "pred_interval = np.concatenate((fct.asnumpy() - 1.65*sigph,\n",
    "                                fct.asnumpy() + 1.65*sigph),axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_forecast_interval(observed, fitted, forecasted, interval):\n",
    "    plt.plot(fitted.asnumpy(), color=\"r\")\n",
    "    plt.plot(observed.asnumpy(), color=\"g\")\n",
    "    T = len(fitted)\n",
    "    plt.plot(np.arange(T, T+len(forecasted)), forecasted.asnumpy(), color=\"b\")\n",
    "    plt.fill_between(np.arange(T, T+len(forecasted)), interval[0,:], interval[1,:])\n",
    "    plt.legend([\"Fitted\", \"Observed\", \"Forecasted\"]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cff62b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_forecast_interval(y,fit,fct,np.transpose(pred_interval))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Numerical forecast distribution\n",
    "\n",
    "In the previous section we derived an analytical distribution for the forecast. This was possible because the model is quite simple and we have made strong assumptions on the distribution of the data. This approach is often not feasible, instead we can resort to numerical simulation to estimate an empirical distribution for the forecast. \n",
    "\n",
    "If we assume that the model we have estimated is the _correct_ model, it is reasonable to assume that our out of sample prediction errors will have the same statistical properties as our in sample prediction errors. \n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_ar1_prediction_interval(last_obs,npred,niter,resid):\n",
    "    fct = nd.zeros((npred,niter))\n",
    "    for i in range(niter):\n",
    "        for j in range(npred):\n",
    "            # resampling the residuals\n",
    "            sample_indices = np.random.randint(resid.shape[0],size = npred)\n",
    "            resamp = resid.asnumpy()[sample_indices,:]\n",
    "            resamp = nd.array(resamp)\n",
    "            if j==0:\n",
    "                fct[j,i] = ar_net(last_obs) + resamp[j,:]\n",
    "            else:\n",
    "                ypred = nd.reshape(fct[j-1,i],shape=(1,1)) \n",
    "                fct[j,i] = ar_net(ypred) + resamp[j,:]\n",
    "    # computing the prediction interval\n",
    "    pred_interval = np.percentile(fct.asnumpy(),q=[5,95],axis=1)\n",
    "    return pred_interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUJxg/H9fZgOU3U57zgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d0ccd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# compute the residuals of the fitted model\n",
    "resid = nd.reshape(y[:train_length], (train_length,1)) - fit\n",
    "pred_interval = gen_ar1_prediction_interval(last_obs,pred_length,1000,resid)\n",
    "plot_forecast_interval(y,fit,fct,pred_interval)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
